discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations abstract nonlinear nonstationary problems arising in elastodynamics have naturally a nonconservative form for these systems it is not possible to define a weak solution according to distribution theory in order to define the concept of discontinuous solutions for these systems one is confronted with multiplications of distributions this is unavoidable from a physical viewpoint since discontinuous solutions are needed to represent shock waves the theory of generalized functions of the second author in which one may multiply arbitrary distributions gives a concept of generalized solutions that may be discontinuous functions existence of such global solutions of the cauchy problem for a system of two equations is proved by a compactness argument from a convergent numerical scheme in the case under consideration the generalized solutions are bounded variation functions the results thus obtained agree with the results expected by the engineers and lead to the development of new numerical schemes

adaptive estimation in a random coefficient autoregressive model this paper proves the local asymptotic normality of a stationary and ergodic first order random coefficient autoregressive model in a semiparametric setting this result is used to show that stein s necessary condition for adaptive estimation of the mean of the random coefficient is satisfied if the distributions of the innovations and the errors in the random coefficients are symmetric around zero under these symmetry assumptions a locally asymptotically minimax adaptive estimator of the mean of the random coefficient is constructed the paper also proves the asymptotic normality of generalized m estimators of the parameter of interest these estimators are used as preliminary estimators in the above construction

moment ratios for absorbing state phase transitions we determine the first through fourth moments of the order parameter and various ratios for several one and two dimensional models with absorbing state phase transitions we perform a detailed analysis of the system size dependence of these ratios and confirm that they are indeed universal for three models the contact process the a model and the pair contact process belonging to the directed percolation universality class our studies also yield a refined estimate for the critical point of the pair contact process

self averaging in the statistical mechanics of some lattice models we discuss self averaging of thermodynamic properties in some random lattice models in particular we investigate when self averaging in an almost sure sense of the free energy implies self averaging of the energy and heat capacity and we discuss the connection between self averaging in the almost sure sense and self averaging in an l p sense under quite general conditions we show that the average of the finite size heat capacity converges to the second derivative of the limiting quenched average free energy we consider the application of these ideas to the problem of adsorption of a random copolymer at a surface and to some related systems

epidemic analysis of the second order transition in the ziff gulari barshad surface reaction model we study the dynamic behavior of the ziff gulari barshad irreversible surface reaction model around its kinetic second order phase transition using both epidemic and poisoning time analyses we find that the critical point is given by p 1 0 3873682 ifmmode pm else textpm fi 0 0000015 which is lower than the previously determined value we also obtain precise values of the dynamical critical exponents z ensuremath delta and ensuremath eta which provide further numerical evidence that this transition is in the same universality class as directed percolation

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

percolation thresholds and fractal dimensions for square and cubic lattices with long range correlated defects we study long range power law correlated disorder on square and cubic lattices in particular we present high precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength the correlations are generated using a discrete version of the fourier filtering method we consider two different metrics to set the length scales over which the correlations decay showing that the percolation thresholds are highly sensitive to such system details by contrast we verify that the fractal dimension d f is a universal quantity and unaffected by the choice of metric we also show that for weak correlations its value coincides with that for the uncorrelated system in two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength approaching d f 2 the onset of this change does not seem to be determined by the extended harris criterion

critical behavior of a three dimensional random bond ising model using finite time scaling with extensive monte carlo renormalization group method we have investigated the critical behavior of a three dimensional random bond ising model for a series of the disorder strength by a finite time scaling combining with monte carlo renormalization group method in the presence of a linearly varying temperature the method enables us to estimate a lot of critical exponents of both static and dynamic nature independently as well as the critical temperatures the static exponents obtained agree well with most existing results verify both the hyperscaling and the rushbrooke scaling laws and their combined scaling law which in turn validate their asymptotic nature and corroborate the universality of the relevant random fixed point with respect to the forms of disorder the dynamic critical exponent z is estimated to 2 114 51 which is compatible with those obtained from experiments and renormalization group analyses the exponents at low and high disorder strengths do not satisfy all scaling laws and are argued to be crossover exponents that reflect crossover from the random fixed point to the pure and the percolation fixed point they also indicate that the exponents that were previously suggested to be a distinct universality class for strong disorder strength in the literature may be just crossover our results demonstrate the effectiveness of the finite time scaling method

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

nonstandard analysis and jump conditions for converging shock waves nonstandard analysis is an area of modern mathematics that studies abstract number systems containing both infinitesimal and infinite numbers this article applies nonstandard analysis to derive jump conditions for one dimensional converging shock waves in a compressible inviscid perfect gas it is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval predistributions of the heaviside function and the dirac delta measure are introduced to model the flow parameters across a shock wave the equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters

testing for randomness in a random coefficient autoregression model abstract we propose a test to discern between an ordinary autoregressive model and a random coefficient one to this end we develop a full fledged estimation theory for the variances of the idiosyncratic innovation and of the random coefficient based on a two stage wls approach our results hold irrespective of whether the series is stationary or nonstationary and as an immediate result they afford the construction of a test for relevant randomness further building on these results we develop a randomised test statistic for the null that the coefficient is non random as opposed to the alternative of a standard r c a 1 model monte carlo evidence shows that the test has the correct size and very good power for all cases considered

a nonlinear conservation law with a step function involving the flux a distributional approach the present paper concerns a riemann problem for a conservation law with a nonlinear flux involving a step function in a convenient space of distributions we will see the emergence of a delta standing wave which extends the corresponding result obtained by sun in 2013 and also by shen in 2014 for a linear flux in the nonlinear setting a new phenomenon arises starting from a vanishing initial condition the concentration of matter in a fixed point becomes possible these results are easy to get essentially because in our approach the product of distributions is a distribution that does not depend of approximation processes the present paper concerns a riemann problem for a conservation law with a nonlinear flux involving a step function in a convenient space of distributions we will see the emergence of a delta standing wave which extends the corresponding result obtained by sun in 2013 and also by shen in 2014 for a linear flux in the nonlinear setting a new phenomenon arises starting from a vanishing initial condition the concentration of matter in a fixed point becomes possible these results are easy to get essentially because in our approach the product of distributions is a distribution that does not depend of approximation processes

multiplications of distributions in elasticity and hydrodynamics it is shown how a mathematical theory of generalized functions in which the multiplications of distributions appearing in nonlinear equations of physics make sense gives new formulas and new numerical results the new methods shown here are quite general but since each particular problem requires its own study this paper is limited to elasticity and hydrodynamics in elasticity hooke s law gives systems in a nonconservative form the study of shock waves for these systems gives nonclassical multiplications of distributions of the form y y heaviside function dirac mass at the origin using this new mathematical tool new formulas are obtained more generally new numerical schemes in a first step ambiguous results are obtained then the ambiguity is removed in hydrodynamics a formulation is obtained that has a nonconservative form and is at the basis of efficient new numerical schemes strictly speaking the reader is not assumed to know anything either on distributions or on elasticity and hydrodynamics since the basic equations are recalled all computations done in this paper are rigorous from the mathematical viewpoint

how to simulate the quasistationary state for a large class of processes with an absorbing state statistical properties of the surviving sample attain time independent values in the quasistationary qs regime we propose a practical simulation method for studying quasistationary properties based on the equation of motion governing the qs distribution in applications to the contact process the method is shown to reproduce exact results for the process on a complete graph and known scaling behavior to high precision at the critical point our method is about an order of magnitude more efficient than conventional simulation

on the universality class of the 3d ising model with long range correlated disorder abstract we analyze a controversial topic about the universality class of the three dimensional ising model with long range correlated disorder whereas both theoretical and numerical studies agree on the validity of the extended harris criterion a weinrib b i halperin phys rev b 27 1983 413 and indicate the existence of a new universality class numerical values of the critical exponents found so far differ considerably to resolve this discrepancy we perform extensive monte carlo simulations of a 3d ising model with non magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice the swendsen wang algorithm is used alongside with a histogram reweighting technique and finite size scaling analysis to evaluate the values of critical exponents governing magnetic phase transition our estimates for these exponents differ from both previous numerical simulations and are in favor of a non trivial dependency of the critical exponents on the peculiarities of long range correlation decay

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

probability distribution of persistent spins in an ising chain we study the probability distribution q n t of n t the fraction of spins unflipped up to time t in an ising chain with ferromagnetic interactions the distribution shows a peak at n nmax and in general is non gaussian and asymmetric in nature however for n nmax it shows a gaussian decay data collapse can be obtained when q n t l versus n nmax l is plotted with 0 45 and 0 6 interestingly nmax t shows different behaviour compared to n t p t the persistence probability which follows the well known behaviour p t t a quantitative estimate of the asymmetry and non gaussian nature of q n t is made by calculating its skewness and kurtosis

new solutions for the one dimensional nonconservative inviscid burgers equation abstract the propagation of travelling waves is a relevant physical phenomenon as usual the understanding of a real propagating wave depends upon a correct formulation of a idealized model discontinuous functions dirac measures and their distributional derivatives are respectively idealizations of sharp jumps localized high peaks and single sharp localised oscillations in the present paper we study the propagation of distributional travelling waves for burgers inviscid equation this will be afforded by our theory of distributional products and is based on a rigorous and consistent concept of solution we have introduced in c o r sarrico distributional products and global solutions for nonconservative inviscid burgers equation j math anal appl 281 2003 641 656 our approach exhibit dirac travelling solitons they are just the infinitesimal narrow solitons of maslov omel yanov and tsupin v p maslov o a omel yanov asymptotic soliton form solutions of equations with small dispersion russian math surveys 36 1981 73 149 v p maslov v a tsupin necessary conditions for the existence of infinitely narrow solitons in gas dynamics soviet phys dokl 24 1979 354 356 and also solutions which are not measures such as for instance u x t b x b t a wave of constant speed b moreover for signals with two jump discontinuities we have in our setting the propagation of more solitons and more values for the signal speed are allowed than those afforded within classical framework

distributions as initial values in a triangular hyperbolic system of conservation laws the present paper concerns the system ut u x 0 vt u v x 0 having distributions as initial conditions under certain conditions and supposing functions we explicitly solve this cauchy problem within a convenient space of distributions u v for this purpose a consistent extension of the classical solution concept defined in the setting of a distributional product not constructed by approximation processes is used shock waves shock waves and also waves defined by distributions that are not measures are presented explicitly as examples this study is carried out without assuming classical results about conservation laws for reader s convenience a brief survey of the distributional product is also included

microscopic profiles of shock waves and ambiguities in multiplications of distributions a rigorous mathematical method is introduced for studying discontinuous solutions for systems in nonconservative form the evidence of the agreement between the theoretical and numerical results is shown on simplified models of physics

optimal inference for instrumental variables regression with non gaussian errors abstract this paper is concerned with inference on the coefficient on the endogenous regressor in a linear instrumental variables model with a single endogenous regressor nonrandom exogenous regressors and instruments and i i d errors whose distribution is unknown it is shown that under mild smoothness conditions on the error distribution it is possible to develop tests which are nearly efficient in the sense of andrews et al 2006 when identification is weak and consistent and asymptotically optimal when identification is strong in addition an estimator is presented which can be used in the usual way to construct valid indeed optimal confidence intervals when identification is strong the estimator is of the two stage least squares variety and is asymptotically efficient under strong identification whether or not the errors are normal

on estimation and adaptive estimation for locally asymptotically normal families locally asymptotically minimax lam estimates are constructed for locally asymptotically normal lan families under very mild additional assumptions adaptive estimation is also considered and a sufficient condition is given for an estimate to be locally asymptotically minimax adaptive incidently it is shown that a well known lower bound due to hajek 1972 for the local asymptotic minimax risk is not sharp

critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder a stochastic cellular automaton exhibiting a parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model this opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state for very strong disorder the model breaks up into blocks with exponential size distribution and continuously changing critical exponents are observed for strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model in which residual particles survive the extinction the critical dynamical behavior of this transition has been explored

violation of scaling in the contact process with quenched disorder we study the two dimensional contact process cp with quenched disorder dcp and determine the static critical exponents beta and nu perp the dynamic behavior is incompatible with scaling as applied to models such as the pure cp that have a continuous phase transition to an absorbing state we find that the survival probability starting with all sites occupied for a finite size system at critical decays according to a power law as does the off critical density autocorrelation function thus the critical exponent nu parallle which governs the relaxation time is undefined since the characteristic relaxation time is itself undefined the logarithmic time dependence found in recent simulations of the critical dcp moreira and dickman phys rev e54 r3090 1996 is further evidence of violation of scaling a simple argument based on percolation cluster statistics yields a similar logarithmic evolution

a geometrical approach to nonconservative shocks and elastoplastic shocks we study systems of conservation laws with convex inequality constraints we analyze shock solutions for the underlying nonconservative system of partial differential equations then we study a model elastoplastic system of partial differential equations in the context of hypoelasticity we show that a sonic point is necessary to construct a compression solution that begins at a constrained compressed state

contact process on a voronoi triangulation we study the continuous absorbing state phase transition in the contact process on the voronoi delaunay lattice the voronoi construction is a natural way to introduce quenched coordination disorder in lattice models we simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice i e that of directed percolation

convergence of numerical schemes involving powers of the dirac delta function abstract developments of the hull elastoplastic numerical method lead to nonconservative versions which in the case of shock waves involve multiplications of distributions of the type of powers of the dirac delta function in the one dimensional case of the shock wave equation u t uu x 0 the numerical solutions will converge to the solution of a different equation if the convergence and the latter equation are considered within the nonlinear theory of generalized functions introduced recently by the second author the study of this phenomenon presented here in one of its relevant particular cases offers for the first time a rigorous understanding of important similar situations encountered in industrial applications when numerical solutions may show either agreement with or deviations from the expected solutions

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

a numerical study of self averaging in adsorption of random copolymers and random surfaces numerical studies involving random copolymers and random surfaces assume self averaging of thermodynamic and metric properties of the systems to calculate different properties for the problem of adsorption of a random copolymer rigorous proofs regarding self averaging of some properties such as free energy in the thermodynamic limit n exist this says little about the extent of self averaging for finite size systems used in numerical studies for the problem of adsorption of a homopolymer on a random surface no analytical proofs regarding self averaging exist in this work assumptions of self averaging of thermodynamic and metric properties of a self avoiding walk model of random copolymer adsorption are tested via multiple markov chain monte carlo method numerical evidence is provided in support of self averaging of energy heat capacity and the z component of the self avoiding walk in different temperature intervals self averaging in energy of a homopolymer interacting with a random surface is also examined

optimal tests of noncorrelation between multivariate time series the problem of testing noncorrelation between two multivariate time series is considered assuming that the global process admits a joint vector autoregressive var representation noncorrelation between the two component series is equivalent to the hypothesis that all off diagonal blocks in the matrix coefficients and the innovation covariance of the joint var representation are zero we establish an adequate local asymptotic normality lan property for this var model in the vicinity of noncorrelation this lan structure allows construction of optimal pseudo gaussian tests that is tests that are locally and asymptotically optimal under gaussian innovations but remain valid under non gaussian ones for the null hypothesis of noncorrelation and for comparing their local asymptotic powers with those of the heuristic tests haugh el himdi roy and koch yang hallin saidi proposed in the literature

quenched bond dilution in two dimensional potts models we report a numerical study of the bond diluted two dimensional potts model using transfer matrix calculations for different numbers of states per spin we show that the critical exponents at the random fixed point are the same as in self dual random bond cases in addition we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin spin correlation function in the cylinder geometry we show that the behaviour is fully compatible with the one observed in the random bond case confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder dilution self dual binary random bond self dual continuous random bond

absorbing state phase transitions exact solutions of small systems i derive precise results for absorbing state phase transitions using exact numerically determined quasistationary qs probability distributions for small systems analysis of the contact process on rings of 23 or fewer sites yields critical properties control parameter order parameter ratios and critical exponents z and ensuremath beta ensuremath nu ensuremath perp with an accuracy of 0 06 or better precise results are also obtained for the pair contact process the qs distribution yields insights on the statistical entropy of these models preliminary application to a model in the stochastic sandpile class is also described

equivalence of conditional and external field ensembles in absorbing state phase transitions i comment on the relation between two sampling methods for absorbing state models it is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external field the actual physical processes involved are identical and the derivation of the identity of the scaling behavior relies on a single established scaling law while the conditional ensemble by construction does not contain information about the system with large external field it contains all the information about the limit of vanishing external field and about the vicinity of the critical point finite size scaling as well as critical scaling in the temperature like variable or in small external field

on the topological phase transition of the two dimensional xy model on the voronoi delaunay lattice we numerically investigate the static properties of the two dimensional 2d xy model on the voronoi delaunay lattice with average connectivity the critical temperature magnetization and vortex density are obtained for instance in this lattice the critical temperature above which free vortices take place reads tvdcr 1 22 in units of j the exchange constant higher than their counterparts for regular square tslcr 0 79 and triangular lattices ttlcr 1 156 with constant connectivity given by 4 and 6 respectively such results lead us to argue that not only the connectivity number but also how the sites are distributed and linked among themselves is also important for determining these physical quantities

the elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions one dimensional collisions between two isotropic solids in which the equations of physics lead to multiplications of distributions are considered based on this example a general physicomathematical method to be adapted to each particular case is proposed to resolve the ambiguity inherent in such products this can be achieved with the aid of a new mathematical theory of generalized functions which permits dealing with mathematical phenomena of a microscopic nature that govern products of distributions having singularities at the same point this tool has recently been applied in various situations in continuum mechanics in which the equations of physics lead to heuristic products of distributions one obtains new algebraic formulas in the simplest cases and new numerical schemes in more general cases the key to the resolution of ambiguities lies in more precise statements of the laws of physics than are permitted within distribution theory and have no analog in classical analysis so that in general a resolution cannot be obtained from formal calculations

distributional products and global solutions for nonconservative inviscid burgers equation abstract burgers equation for inviscid fluids is a simplified case of navier stokes equation which corresponds to euler equation for ideal fluids thus from a variational viewpoint burgers equation appears naturally in its nonconservative form in this form a consistent concept of a weak solution cannot be formulated because the classical distribution theory has no products which account for the term u u x this leads several authors to substitute burgers equation by the so called conservative form where one has 1 2 u 2 x in distributional sense in this paper we will treat nonconservative inviscid burgers equation and study it with the help of our theory of products also the relationship with the conservative burgers equation is considered in particular we will be able to exhibit a dirac travelling soliton solution in the sense of global solution applying our concepts solutions which are functions with jump discontinuities can also be obtained and a jump condition is derived when we replace the concept of global solution by the concept of global strong solution this jump condition coincides with the well known rankine hugoniot jump condition for the conservative burgers equation for travelling waves functions these concepts are all equivalent

critical behavior and griffiths effects in the disordered contact process we study the nonequilibrium phase transition in the one dimensional contact process with quenched spatial disorder by means of large scale monte carlo simulations for times up to 10 9 and system sizes up to 10 7 sites in agreement with recent predictions of an infinite randomness fixed point our simulations demonstrate activated exponential dynamical scaling at the critical point the critical behavior turns out to be universal even for weak disorder however the approach to this asymptotic behavior is extremely slow with crossover times of the order of 10 4 or larger in the griffiths region between the clean and the dirty critical points we find power law dynamical behavior with continuously varying exponents we discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

generalized solutions of nonlinear parabolic equations with distributions as initial conditions abstract we consider the nonlinear parabolic equation u t u u 3 0 in q 0 t t 0 open set in r d d 1 2 with the boundary condition u x t 0 on 0 t and the initial condition u x 0 x in where is the dirac mass at the origin of r it is known that this problem has no weak solution in any known classical sense within the distribution theory using a theory of generalized functions we obtain existence uniqueness and consistence results which describe mathematically the behaviour of the solutions ue obtained with smooth initial conditions u e x 0 e x e d and e when e 0

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

burgers equation with a passive scalar dissipation anomaly and colombeau calculus a connection between dissipation anomaly in fluid dynamics and colombeau s theory of products of distributions is exemplified by considering burgers equation with a passive scalar besides the well known viscosity independent dissipation of energy in the steadily propagating shock wave solution the lesser known case of passive scalar subject to the shock wave is studied an exact dependence of the dissipation rate of the passive scalar on the prandtl number pr is given by a simple analysis we show in particular 1 pr for large pr the passive scalar profile is shown to have a form of a sum of tanh2n 1 x with suitably scaled x thereby implying the necessity to distinguish h from hn when pr is large where h is the heaviside function and n is a positive integer an incorrect result of 1 pr would otherwise be obtained this is a typical example where colombeau calculus for products of weak solutions is required for a correct interpretation a cole hopf type transform is also given for the case o

criticality in the randomness induced second order phase transition of the triangular ising antiferromagnet with nearest and next nearest neighbor interactions abstract using a wang landau entropic sampling scheme we investigate the effects of quenched bond randomness on a particular case of a triangular ising model with nearest j n n and next nearest neighbor j n n n antiferromagnetic interactions we consider the case r j n n n j n n 1 for which the pure model is known to have a columnar ground state where rows of nearest neighbor spins up and down alternate and undergo a weak first order phase transition from the ordered to the paramagnetic state with the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first order phase transition to a second order phase transition and using the lee kosterlitz method we quantitatively verify this conversion the emerging under random bonds continuous transition shows a strongly saturating specific heat behavior corresponding to a negative exponent and belongs to a new distinctive universality class with 1 135 11 1 744 9 and 0 124 8 thus our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional 2d systems without and with quenched disorder

critical behavior of the 3d ising model on a poissonian random lattice abstract the single cluster monte carlo algorithm and the reweighting technique are used to simulate the 3d ferromagnetic ising model on 3d voronoi delauney lattices it is assumed that the coupling factor j varies with the distance r between the first neighbors as j r e a r with a 0 the critical exponents and are calculated and according to the present estimates for the critical exponents we argue that this random system belongs to the same universality class of the pure 3d ferromagnetic ising model

non self averaging in autocorrelations for potts models on quenched random gravity graphs we investigate the non self averaging properties of the dynamics of ising 4 state potts and 10 state potts models in single cluster monte carlo simulations on quenched ensembles of planar trivalent 3 random graphs which we use as an example of relevant quenched connectivity disorder we employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetization in order to discern non self averaging although the specific results discussed here are for quenched random graphs the method has quite general applicability

the riemann problem for pressureless fluid dynamics with distribution solutions in colombeau s sense the riemann problem for the equations of pressureless fluid dynamics was considered solutions of this problem were constructed by employing the viscosity vanishing approach for some initial data solutions showed high singularity around the shock waves a new mathematical theory of generalized functions initiated by j f colombeau was applied to dealing with the multiplication of singular distributions as a byproduct the entropy condition was obtained for singular distribution solutions

evidence of intermittent cascades from discrete hierarchical dissipation in turbulence abstract we present the results of a search of log periodic corrections to scaling in the moments of the square of velocity increments taken as proxies of the energy dissipation rate in experiments at high reynolds number 2500 of three dimensional fully developed turbulence a simple dynamical representation of the richardson kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log periodic corrections to scaling associated with a discrete hierarchy to remedy this drawback we introduce a novel canonical averaging that we test extensively on synthetic examples constructed to mimic the interplay between a weak log periodic component and rather strong multiplicative and phase noises tests are also presented on 1 f5 3 random phase noise on the multifractal random walk model and on lattice and non lattice multifractal models our extensive tests confirm the remarkable observation of statistically significant log periodic corrections to scaling with a preferred scaling ratio for length scales compatible with the value 2 a strong confirmation of this result is provided by the identification of up to five harmonics of the fundamental log periodic undulations associated with up to five levels of the underlying hierarchical dynamical structure a natural interpretation of our results is that the richardson kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales

nonequilibrium relaxation study on spin glass model ferromagnetic fm transition point and universality class of the j ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation ner method at fm bond density p between multicritical one pmc and 1 static exponents take universal values which are different from those of p 1 or p pmc and they are consistent with the values of the random fixed point and of the simulations and experiments for diluted ising systems the dynamical exponent however seems to depend on p and not to be universal although it may be due to finite time correction the estimation of pmc on square lattice is also refined to be 0 8894 9 which is consistent with the nishimori and nemoto s conjecture 0 889972

numerical solutions of one pressure models in multifluid flows flows of a mixture of several fluids can be described by one pressure models their formulation is formally simple and their efficiency has been recognized but from the mathematical viewpoint they present severe peculiarities they are not hyperbolic appear to be ill posed and are in nonconservative form so they show ambiguous products of distributions in case of shock waves a resolution of these ambiguities is proposed it gives jump conditions similar to the classical rankine hugoniot jump conditions of conservative systems this resolution attempts to solve the riemann problem and then the cauchy problem by godunov type schemes following nonconservative techniques initiated by a y le roux and collaborators

universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters percolation models with multiple percolating clusters have attracted much attention in recent years here we use monte carlo simulations to study bond percolation on l1xl2 planar random lattices duals of random lattices and square lattices with free and periodic boundary conditions in vertical and horizontal directions respectively and with various aspect ratios l 1 l 2 we calculate the probability for the appearance of n percolating clusters w n the percolating probabilities p the average fraction of lattice bonds sites in the percolating clusters n n and the probability distribution function for the fraction c of lattice bonds sites in percolating clusters of subgraphs with n percolating clusters f n c b f n c s using a small number of nonuniversal metric factors we find that w n p n n and f n c b f n c s for random lattices duals of random lattices and square lattices have the same universal finite size scaling functions we also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios

newton s second law and the multiplication of distributions newton s second law is applied to study the motion of a particle subjected to a time dependent impulsive force containing a dirac delta distribution within this setting we prove that this problem can be rigorously solved neither by limit processes nor by using the theory of distributions limited to the classical schwartz products however using a distributional multiplication not defined by a limit process a rigorous solution emerges