the high - quality volumetric reconstruction is the common aim in many of the modern imaging modalities .a number of issues are casually packed in the term ` high quality ' , ranging from the suppression of the noise and of occasional artefacts to the enhancement of the contrast and spatial resolution .the dynamic range of the detectors , which are used in the data acquisition , is strongly linked to many of these issues .matsinos and kaissl ( 2006 ) describe a method to calibrate one of the operation modes of flat - panel detectors ( fdp ) manufactured by varian medical systems , inc .( vms ) , palo alto , ca ; that mode had been developed as a response to the need for increasing the dynamic range of the vms x - ray detectors .the present paper introduces an alternative approach which is general and simple enough to implement in a variety of fdp types ; a patent application , relating to this method , is currently under reviewing , see dasani ( 2006 ).  the dual - dose imaging technique may be outlined as follows .two x - ray exposures of an object are obtained at different dose levels . although this technique might also be used in case of scans in the future ( via an implementation similar to the one proposed in eberhard ( 2005 ) in dual - energy imaging ) , these exposures are currently static ( no gantry movement ) , the irradiated object occupying a fixed position in space .digitised images , corresponding to the two exposures , are obtained with the use of an x - ray detector . the first dose level is selected in such a way as to yield a good - quality signal in the high - attenuation areas of the projected image ( onto the detector ) . due to limitations in the range of the output signal ( dynamic range of the detector ) ,it is inevitable that the pixel signal in this high - dose image will saturate in the low - attenuation areas of the projected image ; in most cases , the low - attenuation areas correspond to the contour of the irradiated object .the second dose level is chosen in such a way as to avoid saturation within the projected image , keeping at the same time the dose as high as possible ( to suppress noise ) . finally , the two images are combined and create one image with good - quality information in its entirety .the low - noise high - dose pixel signal is used wherever reliable ( not saturated ) ; otherwise , it is substituted by the low - dose pixel signal after the latter has been scaled by a factor which is determined on the basis of the two input images .given the geometry of an imaging unit , the delivered dose is a function of the x - ray - tube ( simply called ` tube ' hereupon ) voltage , tube current and pulse width .a variation of the voltage in the two exposures induces physical effects which can only be accounted for by a dedicated calibration of the imaging unit , similar to the one developed by matsinos and kaissl ( 2006 ) in the case of the dual - gain mode ; for instance , the scatter contribution and beam - hardening effects are energy - dependent .although the technique of the dual - energy imaging was originally proposed ( as a means to visualise simultaneously different parts of the anatomy ) about twenty years ago , the research interest in this domain has hardly diminished ; the corroboration of this interest is manifested by the amount of patent applications which are currently under reviewing , e.g. , see kump and odogba ( 2003 ) , jabri ( 2004 ) and zhao ( 2004 ) . on the other hand , by varying either the current or the pulse width , one modifies the _ number _ of incident photons , not their energy ; due to this reason , the implementation of an intensity - variation scheme constitutes a less demanding problem . on the technical side ,the solution which is assumed in the vms imaging units pertains to the variation of the intensity of the incident beam via changes induced in the width of the x - ray pulses .this is the reason why the terms ` short pulse ' , ` long pulse ' and ` dual pulse ' are often used in the vms nomenclature as synonyms of ` low dose ' , ` high dose ' and ` dual dose ' , respectively ; in the present paper , we will make use of the latter terms .the data analysed here has been acquired at the vms laboratory in baden , switzerland .the ` on - board imager ' system , comprising the imaging unit of a vms machine which was recently constructed and put into operation to enable image - guided radiation therapy , has been used .the detailed description of this system may be obtained directly from the website of the manufacturer ( ` www.varian.com ' ) .the x - ray source is the vms model g242 ; it is a rotating - anode x - ray tube with maximal operation voltage of kv .the tube is driven and controlled by the x - ray generator . in the modedescribed herein , the generator has been programmed to trigger two x - ray pulses in succession , the short pulse preceding the long one .the vms paxscan 4030cb amorphous - silicon fpd , which is currently used in the data acquisition , is a real - time digital x - ray imaging device comprising square elements ( pixels ) and spanning an approximate area of  . in order to expedite the data transfer and processing , the so - called half - resolution ( -binning ) modeis normally used ; thus , the detector is assumed to consist of ( logical ) pixels ( pitch :  m ) . due to the high sensitivity of the scintillating material ( thallium - doped cesium iodide ) and to sophisticated noise - reduction techniques, the low - dose imaging performance of this type of detector is remarkable , save for a small band ( mm wide ) neighbouring its borders ( ` inactive area of the detector ' ) .the digitisation depth of this fpd type is bits . in reality , however , nonlinear effects are introduced at signals far below the -bit limit . a thorough method to determine accurately the threshold value ( the highest pixel signal which still fulfills the dose - signal linearity ) for each pixel separately has been described in matsinos and kaissl ( 2006 ) . in the present paper, one constant ( same for all pixels ) threshold will be extracted from the data ; to a good approximation , this number is equal to the minimal of the values of the threshold map . in the data processing ,if a pixel signal exceeds this constant threshold value , the pixel will be assumed saturated .high - quality images are important in a variety of applications . restricting ourselves to medical imaging, an obvious requirement is that anatomic details in the region of interest be discernible as good as possible .as regions of interest frequently lie well within the irradiated objects , high - dose x - ray pulses are needed to probe their structure ; otherwise , the resulting images look grainy and the details are masked by quantum and discretisation noise .evidently , the delivery of high dose is needed in the high - attenuation areas of the irradiated object .unfortunately , the delivery of high dose solves one problem at the expense of creating another ; the low - attenuation areas of the object will not be visible if the delivered dose exceeds the limit which is associated with signal saturation . to conclude , due to limitations in the range of the output signal , the good visualisation of one part of the irradiated object impaired the retrieval of information in another .the dual - dose imaging technique solves the afore - described problem by combining parts of the two images in such a way as to create one image containing useful information in all its entirety .the selective use of parts of the two images allows both the contour of the irradiated object to be clearly visible ( avoiding saturation effects ) and the high - attenuation areas to retain their image quality corresponding to the high - dose image .therefore , the application of the technique results in the increase of the dynamic range of the detector which is used in the data acquisition .one of the main features of the present approach is that the combination of the two images is based on information which is exclusively contained within them ; hence , no additional calibration is needed , that is , beyond the standard calibrations of the dark field ( offset ) and flood field ( flat field , flatness or gain ) which are invariably applied to all images .we now come to the description of the algorithm which is currently implemented .two parameters are involved : hereupon , they will be called ` threshold ' and ` ratio ' ; their values are obtained from the two input images .the threshold value determines whether the low- or the high - dose information is to be used in the combination of the two images ; the ratio value determines the amount by which the low - dose image is to be scaled whenever it is used . in the combination of the two images ,the norm is assumed to be the high - dose image .the threshold values obtained in the present paper are offset corrected ; this is due to the fact that the input data have been corrected for offset and gain effects .  in order to extract the threshold from the input data ,the following steps are taken .  1.  the ratio ( high - to - low - dose ) of the pixel signals ( corresponding to the same position on the detector ) in the two images is histogrammed in bins of the high - dose signal ; an average value is obtained in each bin . to safeguard against the introduction of noise , bins with less than ten contentsare ignored .an example of one such distribution is shown in figure [ fig : ratiovshighdose ] .we observe that the ratio of the pixel signals is constant over a wide range of values of the high - dose signal , rapidly dropping at the place where signal saturation sets in . 2 .the derivative of the ratio distribution is subsequently obtained ( figure [ fig : derivative ] ) .the use of the derivative has advantages , namely , the riddance of possible slope effects in the original histogram and larger sensitivity in the area where the ratio of the pixel signals departs from constancy .the threshold is obtained from the derivative plot as follows .let us assume that an average of ratio - derivative values and an rms ( standard deviation ) have been calculated from a number of successive entries ( bins ) ; we will refer to these values as ` current ' .the value corresponding to the next bin in the plot ( with increasing high - dose signal ) is tested for constancy on the basis of the current average and rms ; in case that the difference ( of the bin value to the current average ) is larger than fivefold the current rms ( i.e. , corresponding to a effect for the normal distribution ) , the procedure terminates and the signal which is associated with the lower bound of the bin tested is originaly assigned to the threshold .the starting point in this iterative scheme is assumed to be the average and the rms calculated from the first ten entries ; therefore , the eleventh bin is the first one to be tested for a possible deviation from constancy .the scanning of the derivative plot is done from left ( low values of the high - dose signal ) to right ( high values of the high - dose signal ) .the ratio - derivative plot is finally scanned backwards ( decreasing high - dose signal ) starting at the threshold determined in the previous step . a sign change in the difference of the bin value to the current average ( compared to the sign of the corresponding difference in the case of the originally - assigned threshold ) marks the position of the highest signal which still fulfils the linearity condition .this approach safeguards against several effects , including the existence of an occasional slope in the original plot ( figure [ fig : ratiovshighdose ] ) , a drift in the average and rms values extracted on the basis of figure [ fig : derivative ] , etc .the method is robust ; we are not aware of cases in which it failed to yield a reasonable output .  in the implemented solution in the dual - dose imaging , the high - dose imageis returned in case that no saturation could be detected ( for example , as a result of the selection of inappropriate dose levels in the data acquisition ) .the optimal ratio of the pixel signals is subsequently obtained for all those pixels whose high - dose signal is below threshold ( hence , unsaturated ) . such a distribution is shown in figure [ fig : ratio ] ; in case of less than ten entries , the bin values are neither shown nor taken into account in the statistics .the average of the distribution is obtained and used in the combination of the two images ; the distribution of figure [ fig : ratio ] yields an average value of and an rms of . in an ideal world , devoid of noise ( quantum , readout , electronic , etc . ), the ratio distribution should be a ` -function ' .having determined the threshold and ratio values , we can now proceed to the combination of the two images .our strategy may easily be described in one sentence .if the pixel signal in the high - dose image is below the threshold , it is directly used ; otherwise , it is substituted by the low - dose pixel signal after it has properly been scaled by the optimal ratio determined at the end of the previous section .the combination of the two images may easily be understood with the help of figure [ fig : dataprocessing ] .the high - dose signal ( line ( a ) ) is used in area a ( where it is smaller than the threshold ) ; the low - dose signal ( line ( b ) ) is used in area b ( where the high - dose signal is useless ) .finally , the combined image is constructed in the basis of the straight line om ; in the first segment ( oz ) , the high - dose signals are used , whereas in the second one ( zm ) , the low - dose signals are involved , along with the optimal ratio .evidently , the dynamic range of the output signal ( proportional to the length om ) is larger than the one corresponding only to the high - dose information ( proportional to the length oz ) .the improvement in the image quality when using the dual - dose imaging technique is demonstrated in figure [ fig : headphantom ] .two images of a head phantom were taken at kv and ma ; the pulse - width settings were : msec for the low - dose image and msec for the high - dose image .figures [ fig : ratiovshighdose]-[fig : ratio ] actually correspond to the analysis performed on these two images .the ` theoretical ' ratio of the pixel signals is expected to be equal to ( ratio of the two pulse widths used ) , yet it came out closer to ( figure [ fig : ratio ] ) due to the fact that the acquisition pulse - width settings do not exactly match the properties of the actual pulses which are produced by the generator .it is evident from figure [ fig : headphantom]a that the low - dose image is grainy ; this is a good example of signal degredation as a result of quantum and discretisation noise .the high - dose image shown in figure [ fig : headphantom]b does not suffer from this effect . on the other hand ,the contour of the irradiated object is nicely reproduced in the low - dose image ( figure [ fig : headphantom]d ) ; due to signal saturation , this is the place where the high - dose image fails ( figure [ fig : headphantom]e ) .the images shown in figures [ fig : headphantom]c and [ fig : headphantom]f correspond to the combination of the two images .the window and level parameters have been adjusted in figures [ fig : headphantom ] in such a way as to demonstrate the usefulness of the approach described in the present paper . in this example , the use of the two input images was quite balanced : of the low - dose image is taken over in the combined image , of the high - dose image is used .evidently , details can be simultaneously seen both in the high- and low - attenuation areas of the irradiated object in the combined image .the present paper introduces a method to increase the dynamic range of x - ray detectors which are used in imaging .the input data comprise two fully - corrected ( for offset and gain effects ) x - ray images of an object , obtained at different dose levels . in the current implementation, the intensity modulation is achieved through a variation of the width of the x - ray pulse ; another option would be to vary the x - ray - tube current , or simultaneously both acquisition settings .the data of the two input images are processed and finally yield the values of two parameters : the first parameter defines the level at which the switching from the high- to the low - dose information will occur in the combination of the two input images , whereas the second represents the amount by which the low - dose image will be scaled whenever it is used . a robust method is proposed to extract reliably the values of these two parameters from the input images .the novelty of the approach relates to the fact that the parameters , needed in the combination of the input images , are determined exclusively from the information these images contain ; therefore , no additional calibrations ( save for the standard ones , leading to the offset and gain corrections ) are needed .finally , one image is created , containing signals which are selectively obtained from either of the input images ; the dynamic range of the output image is larger than the one corresponding to the input images ( which is characterised by the limitation in the discretisation depth of the detector ) .the final image contains useful information in all its entirety .the selective use of parts of the two input images allows both the contour of the irradiated object to be visible and the high - attenuation areas to retain their image quality corresponding to the high - dose image .the benefits of the method have been convincingly demonstrated with an example involving a head phantom .         the ratio of the pixel signals histogrammed in bins of the high - dose signal .the vertical dotted line corresponds to the threshold determined on the basis of an analysis of figure [ fig : derivative].,height=585 ]    the strategy followed in the combination of the two images in schematic form .up to the point where the high - dose signal ( line ( a ) ) saturates , it is used ( oz segment ) . above the threshold value ,the low - dose signal ( line ( b ) ) is used properly scaled ; the scaling is done in such a way as to map point m onto m.,width=585 ]  the low - dose ( a and d ) and high - dose ( b and e ) images of the head phantom , along with the combined image ( c and f ) . to show the usefulness of the approach proposed herein ,the level and window values have been adjusted in such a way as to emphasise the details in the interior ( a , b and c ) , as well as those close to the contour of the irradiated object ( d , e and f ) .the degradation of the low - dose image is obvious in the interior of the image ( a ) , while the high - dose image fails close to the contour of the irradiated object ( e ) .the combined image reveals simultaneously the details in the interior ( c ) and around the contour of the irradiated object ( f ) .the data in the inactive area of the detector are not shown in the case of the combined image ( black borders).,width=585 ]

Abstract: we describe a method aiming at increasing the dynamic range of x - ray detectors . two x - ray exposures of an object are acquired at different dose levels and constitute the only input data . the values of the parameters which are needed to process these images are determined from information contained in the images themselves ; the values of two parameters are extracted from the input data . the two input images are finally merged in such a way as to create one image containing useful information in all its entirety . this selective use of parts of each image allows both the contour of the irradiated object to be visible and the high - attenuation areas to retain their image quality corresponding to the information contained in the high - dose image . the benefits of the method are demonstrated with an example involving a head phantom . +  _ keywords _ : cone - beam ct , flat - panel detector , image quality , dual dose , dual pulse +


fragmentation is a term commonly used to specify a nuclear disassembly by force .hot fragmentation is meant to indicate the most violent of these processes , following excitations beyond the limits of nuclear binding , but still ending with bound nuclear fragments of different sizes in the final channels .the formation mechanism of these fragments , whether they are the remnants of an incomplete destruction or the products of a condensation ( selforganization , cf . ) out of the disordered matter , has continued to be the topic of very active research in recent years .a two - stage scenario has proven to be fruitful for the interpretation and modelling of hot - fragmentation reactions .it is motivated by the differences of the wave lengths and time scales governing the entrance and exit channels and justified by the remarkable success of statistical approaches for the second stage .the intermediate states are not necessarily equivalent to hot nuclei but should be , more generally , viewed as systems of highly excited nuclear matter , populating a phase space characterized by global quantities like mass , charge , energy , density or temperature .molecular - dynamics calculations can now continuously follow the reaction process from the first encounter to the final disassembly stages without the need to specifically assume equilibration . in that sense , they present a challenge to the statistical two - stage picture . on the other hand, the extraction of thermodynamical parameters from transport - model calculations has demonstrated that a connection to the statistical approach can be established .there is little doubt that the densities are low and the temperatures high in the intermediate state , coinciding with the values predicted for the coexistence region of liquid and gaseous nuclear matter . to search for observable links of the multifragmentation phenomenon to the predicted phase transitionhas therefore been a major motivation for many experimental and theoretical activities .it is evident from the titles and abstracts submitted to this conference that there is growing confidence that signals of this phase transition are actually being observed .au targets : average mass loss in the fast cascade ( top ) and relative probability for excitation energies ( bottom ) as a function of ( from ref . ) . ]this talk divides into three main parts : a brief review of the reactions that are being used to produce hot nuclear systems , a discussion of the caloric curve of nuclei as a potential signature of the liquid - gas phase transition in finite systems , and new experimental results for the conditions at breakup in spectator reactions .this last part will mainly reflect recent activities of the aladin collaboration .thermal fragmentation denotes a concept of studying the breakup of thermally excited nuclear systems formed in collisions of relativistic hadrons with heavy target nuclei .it is based on the expectation , tested with intranuclear - cascade calculations , that light energetic projectiles will generate a statistical ( thermal ) disorder without exciting collective modes such as compression , rotation or shape deformations .the latter are known to break nuclei very efficiently , and thus would mask the nuclear response to the thermal excitation .the potential and the limits of this approach have been explored by the isis collaboration in their recent experiments at the ags in brookhaven with a variety of primary and secondary beams including pions and antiprotons in the momentum range up to 14.6 gev / c .the properties of intermediate systems produced in these reactions are summarized in fig .target - like residues with several hundreds of mev excitation have the largest cross sections , but excitation energies exceeding 1 gev can be reached , even though with rapidly dropping cross sections .there is also a loss of mass caused by the heating mechanism at relativistic energies .some of the nucleons participating in the cascading processes are too energetic to remain part of the intermediate system .au targets : distribution of fragment multiplicities , parameter describing the element distribution , radial flow energy , and emission time scale ( from top to bottom ) . ref .11 in the bottom panel refers to ( from refs . ) . ]the multi - fragment channels open up at the higher excitation energies , as illustrated in fig .2 . the transition from residue production to hot fragmentation , highlighted by the dotted vertical lines , is , most notably , associated with a striking decrease of the emission time scales to values in the vicinity of 50 fm / c .  according to fig .1 , the most efficient projectiles are antiprotons of high momentum which only are difficult to use because of their low abundance in the secondary beam .some extra heating is generated by the pion cascades from the annihilation which leads to considerable excitation energies already at much lower momenta .the reported fragment multiplicities , however , are significantly smaller for the less energetic antiproton beams even if identical bins of excitation energy are selected .it is therefore an open question whether the excitation energy by itself is the only parameter that governs the decay properties and fragment production .similar questions have recently been raised by other authors who find fewer fragments in the experiment than are predicted by statistical models . while this may be partly connected to the difficulties inherent with experimentally determining the thermalized excitation energy , it is nevertheless obvious that the solution to this problem will help us to better understand how fragments are formed .( top ) and isotope temperature ( bottom ) as a function of for the reaction on au , cu , al and c targets at 600 amev .note that the experimental trigger suppresses the very peripheral collisions at 65 which have much larger cross sections than indicated here ( from ref . ) . ]the limits of generating excitation energy can be overcome with composite projectiles .systematic sets of data with projectiles of different mass and energy have been collected by the fasa , eos and kek / himac collaborations , and new results are reported in contributions to this conference .the continuing rise of the cross section for high excitations with increasing mass of the collision partner is demonstrated in fig . 3 for the fragmentation of projectiles studied by the aladin collaboration .these data are shown as a function of the variable , representing the sum of the atomic numbers of all projectile fragments with 2 , which is inversely correlated with the excitation energy .as an example of the scaling , a prominent feature of spectator reactions up to very high energies , the isotope temperatures are also given in the figure .they are close to 6 mev for the major part of the range , but tend to higher values at low , i.e. at the highest excitation energies reached in these reactions .the temperatures depend only on but not on the specific target that is used to fragment the projectile .large systems at even higher excitations can be produced in central collisions of heavy systems . in this case , the idea of excitation as a simple heating process has to be abandoned , however .collective modes , compression as well as the directed outward motion of particles and clusters from primary collisions generate an explosive pattern , quantified as collective radial flow .the production of large clusters is rare and inversely correlated with the observed amount of flow .an extreme case , observed at the ags , has been reported very recently .for beams of 11.5 gev / c per nucleon , centrally colliding with heavy targets , the fragment mass yields are steeply exponential with a penalty factor of about 50 for each additional mass unit .the characteristic transition from power law to exponential spectra , as radial flow sets in , has been reproduced with molecular dynamics calculations , very recently e.g. with quantum molecular dynamics , but to fully understand the clusterization mechanism in the dynamical environment still remains an interesting problem for future research .heavy symmetric systems below the threshold of collective radial flow ( about 50 mev per nucleon ) have been extensively studied by the miniball / multics and indra collaborations .high - statistics data permit the selection of single - source formation which occurs with small cross sections in central collisions . in more peripheral encounters ,several sources contribute to the fragment yields with a clear enhancement in the mid - rapidity domain . the potential mechanisms of mid - rapidity emissions , as e.g. neck formation , and the isospin effects associated with it are closely connected to several dynamical and statistical aspects of hot fragmentation , among them the isotopic separation expected in the liquid - gas coexistence zone .these topics are the subjects of other plenary talks at this conference .it is commonly accepted that extended nuclear matter should exhibit a liquid - gas phase transition , following from the van - der - waals - like range dependence of the nuclear force .sharp discontinuities in the infinite system are expected to broaden as the system size decreases .this , however , does not contradict the existence or prevent the identification of phase transitions in small systems with constituent numbers on the nuclear scale .mg , , and ( left panel ) and time - averaged radial density distributions of mg at various excitation energies in the coexistence region ( right panel ; from ref . ) . ]the appropriate experiment for identifying the liquid - gas phase transition in finite nuclei has recently been done , theoretically .fermionic as well as antisymmetrized molecular dynamics ( fmd , amd ) models were used to study the equilibrium dynamics of small nuclear systems .none of the necessary ingredients were missing in these studies , a container to confine the system , a controllable heating technique , long propagation times to allow the system to settle into equilibrium , and a suitable technique of measuring the temperature . as a remarkable resultit was shown that the nuclear dynamics , as represented in these advanced transport - type models , generate a phase transition without any further assumptions .caloric curves obtained in the fmd study are shown in fig .4 . the extracted temperatures exhibit a plateau that extends over about 8 mev per nucleon of excitation energy and has its origin in the coexistence of liquid and nuclear phases in the system .the densities reflect the transition from a liquid phase in equilibrium with its surrounding vapor to the pure vapor phase .the properties of the system in these asymptotic states were identified as those of a fermi liquid and a fermi gas ( van - der - waals gas in the amd ) .both groups have also demonstrated that the external conditions , the container which controls the pressure , have a strong influence on the properties of the transition .changing the confinement gives the possibility to map out the phase diagram .the latent heat of the system approaches zero at 10 mev which may be associated with the critical temperature for that system .there is no external confinement in the real experiment , and the time scales of hot - fragmentation reactions are rather short .it is therefore even more surprising that the temperature - energy correlation measured for the breakup states exhibits such a similar behavior . the data for fragmentation shown in fig .5 represent the results for 600 mev per nucleon , with small modifications due to additional experimental information and corrections , and the results for 1000 mev per nucleon obtained more recently .the temperature of the transition region is close to that obtained with the dynamical or statistical models and does not change with the bombarding energy .in contrast to it , the energy associated with the spectator source increases by , on the average , 30% over the range 600 to 1000 mev per nucleon , a behavior inconsistent with the universality of the spectator decay that so clearly appears in other variables .it is caused by the energy dependence of the mean kinetic energies of nucleons in the spectator frame and most likely indicates that contributions from the early stages of the reaction have been included in the calorimetry for the spectator source . as a consequence , the apparent latent heat deduced even for the lower energy of 600 mev per nucleon should be considered as an upper limit .au on collisions .the temperatures were determined from helium and lithium isotope ratios of projectile fragments at 600 amev and of target fragments at 1000 amev ( from ref . ) . ]breakup temperatures and energy contents of the fragmenting system were measured and correlated by several other groups for a variety of different reactions .the basic methods were identical with some variation in the approximations that had to be made .differences exist , e.g. in whether and how the effects of sequential decays on the temperature were taken into account , whether the neutron multiplicities and kinetic energies were measured or estimated , and whether and how preequilibrium components were identified and explicitly excluded . the last point is part of the bigger problem of identifying and properly selecting the fragmenting source which is crucial .the resulting caloric curves have several features in common but are considerably different in detail . a deviation from the behavior of a fermi liquidis observed for all reactions but at different temperatures between 5 and 7 mev .the slopes are somewhat different and the upbend at high excitations is only seen in the spectator decay ( fig .it is not observed for the other reactions which , however , do not easily lead to comparable excitation energies ( fig .apart from the experimental differences and imperfections , it is the transient nature of the reaction process which most likely prevents a single universal curve to emerge from these studies . to the extent that the equilibrated breakup state is an idealization ,measured fragment yields represent integrals over finite emission times , with pre - breakup and post - breakup contributions varying among different reactions .furthermore , the expansion dynamics may generate transient pressures that are different for different types of hot - fragmentation reactions .the prominent role of the pressure , however , is known from the model experiments .temperatures and excitation energies are only two of the quantities of interest that characterize the breakup states .techniques for determining other breakup parameters have been successfully developed and applied . among them , the density is of particular importance because an expansion to low density is a basic ingredient of the multifragmentation scenario .   as deduced from p - p , p- , and d- correlation functions measured for on reactions at 1000 amev .the rapid decrease of the density with decreasing reflects the changing mass of the spectator source .note the logarithmic ordinate scale ( from ref . ) . ]low densities in agreement with model expectations were recently reported for spectator decays following on reactions at 1000 mev per nucleon .they were deduced from measured correlation functions for proton pairs and for unlike pairs of protons or deuterons in coincidence with particles .the correlation functions were found to exhibit the surprising property that their variation with is rather small , indicating source extensions that do not change dramatically with impact parameter in these reactions .the observed variation of the density with impact parameter is mainly caused by the variation of the mass of the intermediate spectator system ( fig .associated time scales were deduced from the same proton - proton data with the technique of directional analysis .they are rather short , of the order of 20 fm / c , and comparable with the collision time in the entrance channel . while this may indicate that a majority of these protons , selected to have energies of 20 mev in the spectator frame , may originate from early stages of the collision , it is still obvious that hot fragmentation initiated by relativistic projectiles is a fast process .the emission times obtained from fragment - fragment correlations ( fig .2 ) are larger by only a factor of two .  with experimental values for temperatures and densities at hand, the breakup conditions can be displayed in the temperature - versus - density plane , commonly used to characterize the nuclear phase behavior .the three data points ( errors are omitted ) shown in fig . 7 are obtained by correlating the measured temperatures ( figs . 3 and 5 ) with the p - p densities of fig .the resulting trajectory in the phase diagram tends to higher temperatures and lower densities in the more violent collisions .it is important to note that this breakup ( equilibrium ) trajectory is practically orthogonal to the actual reaction trajectory followed by the system as it expands from higher to lower temperatures .the measured breakup conditions are at comparable densities but at temperatures far below the critical point of nuclear matter as obtained in the calculations of refs .they are also below the critical temperature obtained for the finite nucleus from the fmd experiment .the conclusion that the breakup occurs in the coexistence region thus seems justified also from this perspective .alternatively , it may be derived from the observation that multifragmentation populates the partition space predicted for the coexistence region by the statistical models .the answer to the question what causes fragmentation is less obvious .as sketched in the figure , the experimental breakup points are barely inside the adiabatic spinodal of the infinite system . in finite nuclei , this region of volume instability is probably limited to much lower temperatures. the expanding systems therefore seem to fragment before coming even close to it. such a conclusion may appear speculative at present , but the need for systematic studies of the instabilities of finite nuclei is rather obvious .surface modes are an alternative to bulk instabilities . while they are expected to be slow in homogeneous systems , they may be rapidly excited during the early stages of the collision .nuclear systems are predicted to be resilient to gentle surface excitations but not to major distortions following more violent encounters .  additional insight in this direction may come from an improved understanding of the kinetic energy spectra of light particles and fragments . in cases of bulk fragmentation, the slope temperatures extracted from fragment spectra are inconsistent with the chemical temperatures obtained with the double - ratio method .however , for spectator decays at relativistic bombarding energies , it has been shown that these temperature values can be consistently understood if the slope temperatures are assumed to reflect the intrinsic fermi motion , as assumed in the goldhaber model .recent calculations with transport models , which incorporate fermi motion , support this interpretation .the energies of spectator fragments are well reproduced , and the coexistence of qualitatively different internal ( or local ) temperatures and fragment slope temperatures has been demonstrated ( fig .the experimental and theoretical findings suggest that fragments are preformed at an early stage in these collisions ( 50 fm / c ) before they may expand to typical breakup densities . to resolve this apparent contradiction to the filling of the phase space at breakup, the basis of the statistical approaches , is an interesting task for the future .au on collisions .the local nucleon temperature 5 mev is indicated at = 1 , the shaded area represents the range of slope temperatures obtained by applying coalescence to a statistical nucleon distribution ( from ref . ) . ]there are many different ways for transforming cold into hot nuclear matter , and we have learned to exploit their different features in our efforts to understand the fragmentation processes .the question of how fragments are formed , the problem of identifying the dominant mechanisms , has been a recurrent theme during this talk .it continues to be a challenge , even though remarkable progress has been made within the last few years .while this requires a realistic modelling of the dynamics , it does not reduce the statistical approaches in their role and importance . not only is it demonstrated that the instabilities governing the fragmentation fill the phase space , but it is also the statistics and thermodynamics of the process that allow us to establish the connection to the nuclear phase transition .the liquid - gas phase transition continues to act as a major motivation and has inspired wider investigations of phase transitions in small systems , extending beyond the nuclear domain .this more general approach seems extremely interesting and rewarding .the caloric curve of nuclei has been emphasized in this talk , but there are other potential observables , not necessarily less challenging on the experimental side , which will be discussed at this conference and should be further pursued and exploited in the future .the uncertainties associated with the measurement of temperatures have been extensively investigated .the temperature differences seen with different methods have led to new insights into the fragmentation mechanism .experimentally , the bigger challenge probably is the identification of the source and the measurement of its excitation energy at breakup .there will be limitations in how far we can go with the assumption of a well defined breakup configuration .the continuous evolution of the reaction and emission processes may not allow a precise distinction between the equilibrated emissions and those preceding it .  finally, the majority of the data included here has come from elaborate experiments with approximately 4- coverage in the respective source frames .it is a pleasure to just look at such data , and it is gratifying to see the big investments in funds and manpower being justified .moreover , it provides encouragement for those who are presently designing or completing potentially even more powerful detection devices for future research .illuminating and inspiring discussions with my colleagues at the gsi , notably a.s .botvina , h. feldmeier , u. lynen , w.f.j .mller , w. nrenberg , w. reisdorf and c. schwarz are gratefully acknowledged .in addition , i like to thank l. beaulieu , d. durand , t. gaitanos , j. ukasik , k.h .schmidt and v.e .viola for providing me with graphics for the talk and for this manuscript .     for a recent review of the fieldsee , e.g. , proceedings of the international workshop xxvii on gross properties of nuclei and nuclear excitations , hirschegg , austria , edited by h. feldmeier et al .( gsi , darmstadt , 1999 ) .

Abstract: today , we have a variety of reactions at hand that can be used to multi - fragment nuclei . in many of these reactions even several sources of fragments can be discerned and characterized .   there is overwhelming evidence that these sources of fragments are hot . it is already less clear whether heat by itself is sufficient to initiate the fragment decay . what causes fragmentation , and when and how are the fragments ( pre)formed ? these questions have remained as much a challenge as the complementary class of questions to which they are related : what observations derive their significance from the liquid - gas phase behavior of extended nuclear matter ? and , can we observe a phase transition in finite nuclei ?   recent developments , largely coming from complex analyses of data sets measured in 4--type experiments as well as from calculations based on advanced theoretical concepts , will be discussed .


wind farm simulations require intensive computational resources and advanced turbine models in order to capture rich amounts of information such as loads along the blades , aerodynamic forces , and power output accurately . the actuator line model ( alm )is known to depend on a high grid resolution ( on the order of 50 grid points per rotor ) when using large - eddy simulations ( les ) to provide grid - converged results . however , in order to study large wind farms and the associated large - scale properties of coupling with the atmospheric boundary layer , wind farms consisting of many turbines must be considered .when many turbines must be included in the computational domain , fine spatial resolution on each rotor is often not affordable , especially if one wishes to repeat the les varying flow conditions , rotor designs , etc .it is thus of interest to study and better understand the performance of the alm approach when using very coarse discretization ( on the order of 10 les grid - points per rotor diameter ) .it has been seen that power extracted from an alm in les is very dependent on the grid resolution and the width of the kernel used to smear the forces .the wake structures are also affected by means of the spatial filter in the velocity field which is not able to resolve the structures smaller than the grid size .the subgrid - scale closure of the les models the smaller scales of the flow , but because of the spatially filtered velocity may differ from the real unsmoothed velocity , differences of predicted forces and power at the rotor blade can exist. the axial induction can be affected by the smearing of the velocity field .  here , we study the implementation of an alm in coarse simulations ( 14 les grid - points per rotor ) .first , we examine the performance of the alm model for a single wind turbine with turbulent inflow conditions for which detailed wind tunnel experimental data are available .second , a formulation is presented to address differences in power caused by the width of the kernel being used . a single turbine in uniform inflowis studied to document the effect of the smearing kernel on blade loads and power production .the current study uses lesgo , the johns hopkins turbulence research group s large - eddy simulations framework including a recent implementation of the alm . solves the filtered navier - stokes equations for very large reynolds number where denotes spatial filtering , is the velocity , is pressure , is density , is the subgrid scale stress tensor , and is the body force .the code uses pseudo - spectral representation in the two horizontal directions with the third ( vertical ) direction using second - order centered finite differencing .the approach is kinetic - energy conserving .time advancement is done using a second order adams - bashforth scheme .subgrid - scale modeling is based on an eddy viscosity type scale - dependent lagrangian dynamic model .the model represents the deviatoric part of the sgs stress tensor , , as where is the dynamically computed smagorinsky coefficient , is the grid resolution , and is the symmetric part of the resolved velocity gradient tensor .the alm implementation in lesgo incorporates a wind turbine into the navier - stokes equation , see eq .[ eq : ns ] , as a body force term .this body force is calculated dynamically depending on the local velocity at the location of each actuator point .the actuator points are used to calculate the blade forces with a high accuracy before they are projected on the computational grid used to calculate the flow field .lift and drag are calculated based on tabulated airfoil data and then smeared onto the flow field as body forces by means of a gaussian kernel where is the distance from the actuator point , and establishes the width of the kernel .the two turbines used for this study are the turbine used in the experiments from the group at cole polytechnique fdrale de lausanne ( epfl ) which has a 0.15 m diameter , and the nrel 5mw reference , which has a 126 m rotor diameter .the turbine used by the group at epfl is a gws / ep-6030 . . the chord and pitch angle along the blades are found in their previous work .the lift and drag coefficient tables were obtained by using a cambered airfoil , i.e. we used airfoil ( 9 ) from the work by sunada et al . in order to match the wake profiles close to the center of the wake , a nacelle has to be included in the model .power and thrust coefficient curves have been obtained using blade element momentum theory and are shown in figure [ fig : cpct ] .it can be observed that this turbine provides a poor performance in terms of power , i.e. low value , compared to a large scale turbine which operates on a range closer to the betz limit .the thrust coefficient , however , is closer to typical values observed for operational large scale turbines .we now present simulation of a wind turbine with turbulent inflow .we use the experiment from the epfl group , here focusing on the single - turbine case .the inflow condition is matched by using a concurrent - precursor simulation matching the given roughness height and friction velocity of the experiment .the tip speed ratio of the turbine is set to as in the experiment . as a first stepwe compare the current implementation of the actuator line model ( alm ) with and without the effects of the nacelle . herethe les uses a coarse discretization , 14 points across the rotor .the alm has been tested with and without a nacelle and tower modeled as drag objects with coefficients of 1.0 and 0.5 respectively .is the mean velocity at hub - height at the inflow location ( -1d ) . ]figures [ fig : multiplotu ] and [ fig : multiplotupup ] show streamwise velocity and turbulence intensity profiles across the wake for a single turbine in a turbulent boundary layer .the non - dimensional scale used is the hub - height velocity .it is to be noted that in order to obtain good agreement between the experiments and simulations a nacelle model needs to be included .the current implementations provides excellent agreement for the velocity profiles of the wake .the turbulence intensity computed in the les under - predicts the experimental measurements .this is expected from les , since some of the scales are filtered , thus reducing the fluctuations .the overall trends agree quite well , and it can be observed that at 2 - 3d downstream the wake of the nacelle and tower have a big influence in both the mean velocity and turbulence intensity .the wake profiles obtained agree very well with the experiments .however , quantities at the turbine , such as power and thrust , are very dependent on the grid resolution and the value of the kernel width . the power coefficient obtained from the simulation for this turbine is .this power coefficient is significantly higher than what is predicted by the turbine design using bem ( figure [ fig : cpct ] ) . while the overall thrust may be realistic ( since the wake profiles agree well ) , the differences between the predicted and the expected from bem points to possible problems due to the smearing of velocity inherent in alm with very coarse les resolutions . in order to better understand the discrepancy, first we perform a simulation under uniform inflow , and then present some initial thoughts of how the model inaccuracies may be remedied .we consider the simulation of the nrel wind turbine with laminar uniform inflow .we use les with a grid resolution of 4 m in each direction , an inflow velocity of 8 ( m / s ) , a prescribed tip - speed ratio of , and vary the gaussian kernel width .it is known that wind turbine loads along the blades depend significantly on the filtering size of the gaussian kernel used to smear the forces of the turbine .figure [ fig : bem ] shows angle of attack , axial velocity , lift and drag along the blade for an nrel 5mw reference turbine modeled as an actuator line with different kernel widths ( ) .      from this figurewe can see that the largest difference is in axial velocity .this difference will cause differences in the lift and drag curves , that are more pronounced as we move further towards the tip .these differences change the total power that the turbine is extracting from the flow .next , we present some analytical considerations focusing on the effects of the spatial filtering inherent in les and its impacts on the alm computations of forces .we take the lift component of the body force term per unit width in a 2d frame and write it ( simplifying ) as : where is the chord , is the density , is the lift coefficient , and is the magnitude of the local velocity on the reference frame of the moving airfoil section . the coefficient is a function of through its dependence on angle of attack . for small angle of attack , and thus the angle of attackcan be expressed as , where is the axial velocity .the lift coefficient for small angles of attack is given by where is a constant and is an offset .we will assume so that the filtered body force can be defined as now we can also write a similar equation for the unfiltered force : and from here : if we use the argument that the velocity magnitude is dominated by the rotational component of the velocity vector ( which is valid for high tsr s ) then we can take the velocity magnitude out of the filtering operation and we obtain the relationship in eq .[ eq : ratio ] enables us to interpret the results shown in fig .[ fig : bem ] ( top right ) in the sense that the ratio of unfiltered force equals the ratio of unfiltered to filtered _ axial _ velocity .we wish to determine the unfiltered force but only know the filtered force .if we can model ratio of unfiltered and filtered axial velocity , eq [ eq : ratio ] would enable us to determine the correct ( unfiltered ) force .  while the derivation of eq .[ eq : ratio ] was based on spatial filtering , we now interpret variables filtered at a scale as the variables one obtains by running les and alm with a kernel width .while this assumption can not be firmly established on theoretical grounds , in practice it is a useful assumption and is commonly made in les .for example , if we denote the axial velocity and force obtained in a simulation with a kernel as and , and associate the scale with the filtering scale , then and . as a next step ,we filter eq .[ eq : ratio ] at another filter scale and assume that the -variables are not affected by this smaller - scale filtering. then one can rewrite eq . [eq : ratio ] according to we can use simulations performed at various s to test this relationship , as a first step in establishing possible correction strategies for the alm approach .  returning to our simulations of the nrel case , we consider m , and attempt to use the results from the other 4 runs with to rescale the force . if eq .[ eq : ua2 ] holds , the distribution of should coincide with the rhs of eq .[ eq : ua2 ] , i.e. with , regardless of chosen .the first region of the blade is made of cylindrical sections which produce no lift , thus the approach presented is not used in this section . as seen in figure [ fig : ua ] the curves collapse through most of the blade except close to the tip .the reason for this is that near the tip , the 3d effects of the kernel become more noticeable.   values ( left ) and re - scaled axial velocity ( right ) to 8 m case as a function of blade length , where and m. the data points coincide with the actuator points used in the simulation.,title="fig : " ]  values ( left ) and re - scaled axial velocity ( right ) to 8 m case as a function of blade length , where and m. the data points coincide with the actuator points used in the simulation.,title="fig : " ]the alm has been validated on a relatively coarse resolution with experimental measurements from the group at epfl .the les provides good agreement with the experiments , but a nacelle and tower model are required to obtain the proper wake deficit .when analyzing power output computed by the alm , the values are higher than those predicted by blade element momentum theory . a theoretical analysis is presented that attempts to relate filtered forces to filtered velocities , highlighting the impact of filtering of the axial velocity on the force distribution .the derived relationship is tested based on simulations done at various values and is seen to hold rather well , except when approaching the tip of the blade .the results imply that one may be able to predict the fine - grained force corresponding to an smaller than that of the simulation , if one were able to deduce the corresponding axial velocity from the data at coarser .such a model - based defiltering operation is the focus of ongoing investigations .lamt was supported by nsf ( igert ) , while international travel and cm were supported by nsf ( iia 124382 , the windinspire project ) .rjams is supported by the research program fellowships for young energy scientists ( yes ! ) of the foundation for fundamental research on matter ( fom ) supported by the netherlands organization for scientific research ( nwo ) .

Abstract: in this work the accuracy of the actuator line model ( alm ) in large eddy simulations of wind turbine flow is studied under the specific conditions of very coarse spatial resolutions . for finely - resolved conditions , it is known that alm provides better accuracy compared to the standard actuator disk model ( adm ) without rotation . however , we show here that on very coarse resolutions , flow induction occurring at rotor scales can affect the predicted inflow angle and can adversely affect the alm predictions . we first provide an illustration of coarse les to reproduce wind tunnel measurements . the resulting flow predictions are good , but the challenges in predicting power outputs from the detailed alm motivate more detailed analysis on a case with uniform inflow . we present a theoretical framework to compare the filtered quantities that enter the large - eddy simulation equations as body forces with a scaling relation between the filtered and unfiltered quantities . the study aims to apply the theoretical derivation to the simulation framework and improve the current results for an alm , especially in the near wake where the largest differences are observed .