using entropy based methods to study general constrained parameter optimization problems abstract we propose the use of physics techniques for entropy determination on constrained parameter optimization problems the main feature of such techniques the construction of an unbiased walk on energy space suggests their use on the quest for optimal solutions of an optimization problem moreover the entropy and its associated density of states give us information concerning the feasibility of solutions

universal features and tail analysis of the order parameter distribution of the two dimensional ising model an entropic sampling monte carlo study we present a numerical study of the order parameter probability density function pdf of the square ising model for lattices with linear sizes l 80 140 a recent efficient entropic sampling scheme combining the wang landau and broad histogram methods and based on the high levels of the wang landau process in dominant energy subspaces is employed we find that for large lattices there exists a stable window of the scaled order parameter in which the full ansatz including the pre exponential factor for the tail regime of the universal pdf is well obeyed this window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal pdf the probability densities are used to estimate the universal privman fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime

scaling and entropy in p median facility location along a line the p median problem is a common model for optimal facility location the task is to place p facilities e g warehouses or schools in a heterogeneously populated space such that the average distance from a person s home to the nearest facility is minimized here we study the special case where the population lives along a line e g a road or a river if facilities are optimally placed the length of the line segment served by a facility is inversely proportional to the square root of the population density this scaling law is derived analytically and confirmed for concrete numerical examples of three us interstate highways and the mississippi river if facility locations are permitted to deviate from the optimum the number of possible solutions increases dramatically using monte carlo simulations we compute how scaling is affected by an increase in the average distance to the nearest facility we find that the scaling exponents change and are most sensitive near the optimum facility distribution

structure of molecular liquids hard rod disk mixtures the structure of hard rod disk mixtures is studied using monte carlo simulations and integral equation theory for a range of densities in the isotropic phase by extension of methods used in single component fluids the pair correlation functions of the molecules are calculated and comparisons between simulation and integral equation theory using a number of different closure relations are made comparison is also made for thermodynamic data and phase behavior

combination of improved multibondic method and the wang landau method we propose a method for monte carlo simulation of statistical physical models with discretized energy the method is based on several ideas including the cluster algorithm the multicanonical monte carlo method and its acceleration proposed recently by wang and landau as in the multibondic ensemble method proposed by janke and kappler the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number a test on the ising model shows that the number of monte carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size whereas it is proportional to the system size squared for other conventional methods in addition the method shows a better performance than the original wang landau method in measurement of physical quantities

co ordinate transformations for second order systems part i general transformations abstract when the dynamics of any general second order system are cast in a state space format the initial choice of the state vector usually comprises one partition representing system displacements and another representing system velocities co ordinate transformations can be defined which result in more general definitions of the state vector this paper discusses the general case of co ordinate transformations of state space representations for second order systems it identifies one extremely important subset of such coordinate transformations namely the set of structure preserving transformations for second order systems and it highlights the importance of these it shows that one particular structure preserving transformation results in a new system characterized by real diagonal matrices and presents a forceful case that this structure preserving transformation should be considered to be the fundamental definition for the characteristic behaviour of general second order systems in preference to the eigenvalue eigenvector solutions conventionally accepted

three dimensional antiferromagnetic q state potts models application of the wang landau algorithm we apply a newly proposed monte carlo method the wang landau algorithm to the study of the three dimensional antiferromagnetic q state potts models on a simple cubic lattice we systematically study the phase transition of the models with q 3 4 5 and 6 we obtain the finite temperature phase transition for q 3 and 4 whereas the transition temperature is down to zero for q 5 for q 6 there exists no order for any temperature we also study the ground state properties the size dependence of the ground state entropy is investigated we find that the ground state entropy is larger than the contribution from the typical configurations of the broken sublattice symmetry state for q 3 the same situations are found for q 4 5 and 6

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

self similar planar curves related to modified korteweg de vries equation we exhibit a time reversible geometric flow of planar curves which can develop singularities in finite time within the uniform topology the example is based on the construction of selfsimilar solutions of modified korteweg de vries equation of a given small mean

critical end point behavior in a binary fluid mixture we consider the liquid gas phase boundary in a binary fluid mixture near its critical end point using general scaling arguments we show that the diameter of the liquid gas coexistence curve exhibits singular behaviour as the critical end point is approached this prediction is tested by means of extensive monte carlo simulations of a symmetrical lennard jones binary mixture within the grand canonical ensemble the simulation results show clear evidence for the proposed singularity as well as confirming a previously predicted singularity in the coexistence chemical potential fisher and upton phys rev lett 65 2402 1990 the results suggest that the observed singularities particularly that in the coexistence diameter should also be detectable experimentally

understanding and improving the wang landau algorithm we present a mathematical analysis of the wang landau algorithm prove its convergence and identify sources of errors and strategies for optimization in particular we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation and the statistical error is found to scale as sqrt mathrm ln phantom rule 0 2em 0ex f with the modification factor f this has implications for strategies for obtaining fast convergence

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

monte carlo study of the antiferromagnetic three state potts model with a staggered polarization field on the square lattice using the wang landau monte carlo method we study the antiferromagnetic af three state potts model with a staggered polarization field on the square lattice we obtain two phase transitions one belongs to the ferromagnetic three state potts universality class and the other to the ising universality class the phase diagram obtained is quantitatively consistent with the transfer matrix calculation the ising transition in the large nearest neighbour interaction limit has been made clear by the detailed analysis of the energy density of states

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

frequency dependent operations for 2nd order systems modal expansion and modal correlation abstract in this paper two frequency dependent operations for viscously damped systems are presented the first operation comprises a new frequency dependent modal expansion while the second operation generalises a recently proposed modal correlation approach for these systems such that particular frequencies are targeted the two suggested methods are connected by a common method for specifying frequency in a generalised sense and they are each illustrated using numerical examples

total decoupling of general quadratic pencils part i theory abstract the notion of quadratic pencils 2 m c k where m c and k are n n real matrices with or without some additional properties such as symmetry or positive definiteness plays critical roles in many important applications it has been long desirable yet with very limited success to reduce a complicated high degree of freedom system to some simpler low degree of freedom subsystems recently garvey friswell and prells proposed a promising approach by which under some mild assumptions a general quadratic pencils can be converted by real valued isospectral transformations into a totally decoupled system this approach if numerically feasible would reduce the original n degree of freedom second order system to n totally independent single degree of freedom second order subsystems such a claim would be a striking breakthrough in the common knowledge that generally no three matrices m c and k can be diagonalized simultaneously this paper intends to serve three purposes to clarify some of the ambiguities in the original proposition to simplify some of the computational details and most importantly to complete the theory of existence by matrix polynomial factorization tactics

yang lee zeros of triangular ising antiferromagnets abstract in our previous research by combining both the exact enumeration method microcanonical transfer matrix for a small system l 9 with the wang landau monte carlo algorithm for large systems to l 30 we obtained the exact and approximate densities of states g m e as a function of the magnetization m and exchange energy e for a triangular lattice ising model in this paper based on the density of states g m e the precise distribution of the yang lee zeros of triangular lattice ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature a e 2 for a 9 9 lattice system also the feasibility of the yang lee zero approach combined with the wang landau algorithm is demonstrated as a result we obtained the magnetic exponents for triangular ising antiferromagnets at various temperatures

momentum shell renormalization group flow from simulation our recently developed fourier monte carlo algorithm permits a nonperturbative calculation of momentum shell renormalization group flows by simulation which despite its apparent simplicity is illustrative both numerically as well as conceptually interesting we study the example of a varphi 4 model with long range lattice interaction for this model we show that the topology of the renormalization flow is globally accessible in a particularly convenient way the nontrivial fixed point of wilson fisher type is observed its accompanying critical exponents are numerically determined from fitting its surrounding flow pattern to a linearized renormalization group transformation the results are compared to those obtained from perturbation theory expansion and earlier monte carlo simulations application of our method is also expected to be rewarding in other models with long range interactions

critical point and coexistence curve properties of the lennard jones fluid a finite size scaling study monte carlo simulations within the grand canonical ensemble are used to explore the liquid vapor coexistence curve and critical point properties of the lennard jones fluid attention is focused on the joint distribution of density and energy fluctuations at coexistence in the vicinity of the critical point this distribution is analyzed using mixed field finite size scaling techniques aided by histogram reweighting methods the analysis yields highly accurate estimates of the critical point parameters as well as exposing the size and character of corrections to scaling in the subcritical coexistence region the density distribution is obtained by combining multicanonical simulations with histogram reweighting techniques it is demonstrated that this procedure permits an efficient and accurate mapping of the coexistence curve even deep within the two phase region

optimization with extremal dynamics for the traveling salesman problem abstract by mapping the optimization problems to physical systems the paper presents a general purpose stochastic optimization method with extremal dynamics it is built up with the traveling salesman problem tsp being a typical np complete problem as self organized critical processes of extremal dynamics the optimization dynamics successively updates the states of those cities with high energy consequently a near optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations ergodic walk near the phase transition the computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics such as simulated annealing sa since the proposed fundamental solution is based on the principles and micromechanisms of computational systems it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems

avoiding boundary effects in wang landau sampling a simple modification of the wang landau sampling algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm

generalization of the wang landau method for off lattice simulations we present a rigorous derivation for off lattice implementations of the so called random walk algorithm recently introduced by wang and landau phys rev lett 86 2050 2001 originally developed for discrete systems the algorithm samples configurations according to their inverse density of states using monte carlo moves the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties we present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states by constructing a uniform ensemble for configurational degrees of freedom in which all potential energies volumes and numbers of particles are equally probable we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case to demonstrate the generality of our approach we perform sample calculations for the lennard jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor liquid coexistence locus

entropic sampling in the path integral monte carlo method we have extended the entropic sampling monte carlo method to the case of path integral representation of a quantum system a two dimensional density of states is introduced into path integral form of the quantum canonical partition function entropic sampling technique within the algorithm suggested recently by wang and landau wang f and landau d p 2001 phys rev lett 86 2050 is then applied to calculate the corresponding entropy distribution a three dimensional quantum oscillato ri sc onsidered as an example canonical distributions for a wide range of temperatures are obtained in a single simulation run and exact data for the energy are reproduced

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

baxter wu model in the presence of an external magnetic field abstract in this work we study an unusual phase transition of the baxter wu model in the presence of an external magnetic field the model is pure baxter wu which means that only three spin interactions are taken into account we construct a phase diagram on the temperature field plane based mainly on the singularities of the specific heat these singularities are more clearly observed than those of the magnetic susceptibility which are used in existing works we establish a discontinuity in the critical exponents when the field is changed from zero to negative

co ordinate transformations for second order systems part ii elementary structure preserving transformations abstract it has been shown in a previous paper that there is a real valued transformation from the generaln degree of freedom second order system to a second order system characterized by diagonal matrices an immediate extension of this fact is that for any second order system there is a set of real valued transformations thestructure preserving transformations which transform this system to a different second order system having identical characteristic behaviour there are several possible reasons why it may be very useful to achieve a particular structure in the transformed system it is obvious that a diagonal structure is extremely useful and a method has been devised for determining the diagonalizing transformation from the solution of the usual complex eigenvalue eigenvector problem this paper begins by outlining the usefulness of some other structures then it defines a class of elementary structure preserving co ordinate transformations that transform from one n degree of freedom second order system to another the termelementary is applied because any one of these transformations is the minimum rank modification of the identity transformation the changes occurring in the system matrices as a result of the application of one such elementary transformation transpire to be very simple in form they are low rank and they can be computed very efficiently this paper provides the fundamental tools to enable the design of structure preserving co ordinate transformations which transform a second order system originally characterized by three general matrices in stages into a mathematically similar second order system characterized by three diagonal matrices the procedure by which the individual elementary transformations are obtained is still under development and it is not discussed in this paper however an illustration is given of a five degree of freedom self adjoint system being transformed into tridiagonal form

entropic sampling via wang landau random walks in dominant energy subspaces dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution such as the probability density and the fourth order binder s cumulant our analysis generalizes the ideas of the critical minimum energy subspace crmes technique applied previously to study the specific heat s finite size scaling here we illustrate alternatives that are useful for the analysis of further finite size anomalies and the behavior of the corresponding dominant subspaces is presented for the two dimensional 2d baxter wu and the 2d and 3d ising models in order to show that a crmes technique is adequate for the study of magnetic anomalies we study and test simple methods which provide the means for an accurate determination of the energy order parameter e m histograms via wang landau random walks the 2d ising model is used as a test case and it is shown that high level wang landau sampling schemes yield excellent estimates for all magnetic properties our estimates compare very well with those of the traditional metropolis method the relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha nu and gamma nu respectively using the metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the metropolis method to produce a reliable estimation scheme for the tail regime of the order parameter distribution

critical endpoint behavior in an asymmetric ising model application of wang landau sampling to calculate the density of states using the wang landau sampling method with a two dimensional random walk we determine the density of states for an asymmetric ising model with two and three body interactions on a triangular lattice in the presence of an external field with an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite size analyses at and away from the critical endpoint we observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint and the exponents for both divergences agree well with previous theoretical predictions

scaling properties of the baxter wu model abstract we use a recently developed cluster algorithm for the baxter wu model to study characteristic features of its behavior magnetic scaling properties of the model are investigated for second order phase transitions we improve significantly the accuracy of monte carlo simulation results and we provide new results for the behavior of the binder cumulants for temperatures below above and at the critical point

local well posedness for the modified kdv equation in almost critical widehat h r_s spaces we study the cauchy problem for the modified kdv equation u t u xxx u 3 x 0 u 0 u 0 for data u 0 in the space h r s defined by the norm u 0 h r s s u 0 lr local well posedness of this problem is established in the parameter range 2 r 1 s 1 2 1 2r so the case s r 0 1 which is critical in view of scaling considerations is almost reached to show this result we use an appropriate variant of the fourier restriction norm method as well as bi and trilinear estimates for solutions of the airy equation

critical endpoints interfaces and walls abstract the behavior of thermodynamic properties at critical endpoints is discussed and the first results of studies underway in collaboration with p j upton and with m c barbosa are sketched new universal aspects beyond normal bulk criticality appear in singularities of the phase boundary to the spectator phase and in the surface tensions of the corresponding noncritical interfaces mean field theory and more general local free energy functionals can be applied some quantitative estimates are presented for universal surface tension amplitude ratios for two distinct classes of endpoint symmetric and nonsymmetric a promising parametric trigonometric model for the scaled equation of state is mentioned and other approaches are touched upon

regularity of solutions to the schrodinger equation soit f dans l espace de schwartz s r n et soit s t f x u x t rn exp ix exp it 2 f d x r n t r f est la transformee de fourier de f on considere u solution de l equation de schrodinger u i u t on pose s f x sup 0 t 1 s t f x x r n on introduit des espaces de sobolev h s en posant h s f s f hd s s r ou f hd s rn 1 2 s f 2 d 1 2 on etudie pour quelles valeurs de s on a b s f x 2 dx 1 2 c b f hd s f s r n pour toutes les boucles b de r n

critical energy distribution function of the baxter wu model abstract in this work we examine the critical finite size scaling behavior of the energy probability distribution function and its corresponding binder cumulant at critical point based on the results of monte carlo simulations at zero external magnetic field using the recently developed triangle cluster algorithm we calculate the energy distribution function s exponents and we derive the scaling relations for the energy binder cumulant finally we predict the exact form of the scaled energy distribution function most of our conclusions seem applicable not only to the baxter wu model but also to other ising like models

probability changing cluster algorithm for potts models we propose a new effective cluster algorithm of tuning the critical point automatically which is an extended version of the swendsen wang algorithm we change the probability of connecting spins of the same type p 1 e j k b t in the process of the monte carlo spin update since we approach the canonical ensemble asymptotically we can use the finite size scaling analysis for physical quantities near the critical point simulating the two dimensional potts models to demonstrate the validity of the algorithm we have obtained the critical temperatures and critical exponents which are consistent with the exact values the comparison has been made with the invaded cluster algorithm

universality and double critical end points a double critical end point in the two dimensional spin 3 2 blume capel model is studied via extensive monte carlo simulations the resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points

numerical estimation of the asymptotic behaviour of solid partitions of an integer the number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory in this paper solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by monte carlo simulations using wang landau sampling method for integers up to 8000 it is shown that limn ln p3 n n3 4 1 79 0 01 where p3 n is the number of solid partitions of the integer n this result strongly suggests that the macmahon conjecture for solid partitions though not exact could still give the correct leading asymptotic behaviour

structure and stability of isotropic states of hard platelet fluids we study the thermodynamics and the pair structure of hard infinitely thin circular platelets in the isotropic phase monte carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function including nonmonotonical variation of some of the components with density integral equation theory is shown to reproduce the main features observed in simulations the hypernetted chain closure as well as its extended versions that include the bridge function up to second and third order in density perform better than both the percus yevick closure and verlet bridge function approximation using a recent fundamental measure density functional theory an analytic expression for the direct correlation function is obtained as the sum of the mayer bond and a term proportional to the density and the intersection length of two platelets this is shown to give a reasonable estimate of the structure found in simulations but to fail to capture the nonmonotonic variation with density we also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the kerr coefficient vanishes as a reference system we compare to simulation results for hard oblate spheroids with small but nonzero elongations demonstrating that the case of vanishingly thin platelets is approached smoothly

asymptotics frequency modulation and low regularity ill posedness for canonical defocusing equations in a recent paper kenig ponce and vega study the low regularity behavior of the focusing nonlinear schrodinger nls focusing modified korteweg de vries mkdv and complex korteweg de vries kdv equations using soliton and breather solutions they demonstrate the lack of local well posedness for these equations below their respective endpoint regularities in this paper we study the defocusing analogues of these equations namely defocusing nls defocusing mkdv and real kdv all in one spatial dimension for which suitable soliton and breather solutions are unavailable we construct for each of these equations classes of modified scattering solutions which exist globally in time and are asymptotic to solutions of the corresponding linear equations up to explicit phase shifts these solutions are used to demonstrate lack of local well posedness in certain sobolev spaces in the sense that the dependence of solutions upon initial data fails to be uniformly continuous in particular we show that the mkdv flow is not uniformly continuous in the l 2 topology despite the existence of global weak solutions at this regularity finally we investigate the kdv equation at the endpoint regularity h and construct solutions for both the real and complex kdv equations the construction provides a nontrivial time interval t t and a locally lipschitz continuous map taking the initial data in h to a distributional solution u c 0 t t h which is uniquely defined for all smooth data the proof uses a generalized miura transform to transfer the existing endpoint regularity theory for mkdv to kdv

flat histogram monte carlo simulations of triangulated fixed connectivity surface models using the wang landau flat histogram monte carlo fhmc simulation technique we were able to study two types of triangulated spherical surface models in which the two dimensional extrinsic curvature energy is assumed in the hamiltonian the gaussian bond potential is also included in the hamiltonian of the first model but it is replaced by a hard wall potential in the second model the results presented in this paper are in good agreement with the results previously reported by our group the transition of surface fluctuations and collapsing transition were studied using the canonical metropolis monte carlo simulation technique and were found to be of the first order the results obtained in this paper also show that the fhmc technique can be successfully applied to triangulated surface models it is non trivial whether the technique is applicable or not to surface models because the simulations are performed on relatively large surfaces

global well posedness of the one dimensional cubic nonlinear schrodinger equation in almost critical spaces abstract in this paper we first introduce a new function space m h p whose norm is given by the l p sum of modulated h norms of a given function in particular when 1 2 we show that the space m h p agrees with the modulation space m 2 p r on the real line and the fourier lebesgue space f l p t on the circle we use this equivalence of the norms and the galilean symmetry to adapt the conserved quantities constructed by killip visan zhang to the modulation space and fourier lebesgue space setting by applying the scaling symmetry we then prove global well posedness of the one dimensional cubic nonlinear schrodinger equation nls in almost critical spaces more precisely we show that the cubic nls on r is globally well posed in m 2 p r for any p while the renormalized cubic nls on t is globally well posed in f l p t for any p in appendix we also establish analogous global in time bounds for the modified kdv equation mkdv in the modulation spaces on the real line and in the fourier lebesgue spaces on the circle an additional key ingredient of the proof in this case is a galilean transform which converts the mkdv to the mkdv nls equation

modal correlation approaches for general second order systems matching mode pairs and an application to campbell diagrams abstract modal correlation is well developed for undamped and proportionally damped vibrating systems it is less well defined for generally damped linear systems this paper addresses the fundamental problem of comparing two general second order linear systems through modal information it considers precisely the problem of how to achieve matching of modes mode pairs there are several possible motivations for modal correlation of which the most important is probably the model updating application in that application one set of modes derives from a numerical model and the other from measured data this paper focuses mainly on a different application constructing campbell diagrams for rotating machines there are two significant differences here a the two sets of modes being compared at any one time are from the same numerical model but for different spin speeds and b there is generally a strong distinction between the left and right modes of the system without some modal correlation approach the campbell diagram is constructed simply as a set of points on the frequency speed graph with modal correlation the eigenvalue problem can be solved at far fewer speeds and the points can be joined meaningfully a dimensionless n n modal matching array is produced whose entries indicate which pairs of modes from the first system best correlate with any particular pair of modes from the second system the presented work is motivated mainly by the application of developing campbell diagrams for rotating machines by means which are more effective than simply plotting a large set of discrete points wider applications of this paper include model updating procedures where mode pairs must be matched initially to ensure convergence towards the exact system