universal configurational structure in two dimensional scalar models monte carlo methods are used to explore the universal configurational structure of two dimensional spin 1 2 spin 1 and border phi 4 models comparison of spin 1 2 and spin 1 data provides evidence that the magnetisation distribution effectively the helmholtz free energy function and its coupling derivative effectively the internal energy function constitute readily accessible signatures of a universality class it is shown that when allowance is made for relatively large corrections to scaling effects the behaviour of the border phi 4 model may be satisfactorily matched to that of the other two models substantiating the view that the border model does indeed belong to the ising universality class

exact three wave solutions for the kp equation a new type of three wave solution periodic two solitary wave solutions for 1 2 d kadomtsev petviashvili kp equation is obtained using the extended three soliton method and with the help of maple

asymmetry in power law magnitude correlations time series of increments can be created in a number of different ways from a variety of physical phenomena for example in the phenomenon of volatility clustering well known in finance magnitudes of adjacent increments are correlated moreover in some time series magnitude correlations display asymmetry with respect to an increment s sign the magnitude of x i depends on the sign of the previous increment x i 1 here we define a model independent test to measure the statistical significance of any observed asymmetry we propose a simple stochastic process characterized by a an asymmetry parameter lambda and a method for estimating lambda we illustrate both the test and process by analyzing physiological data

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

accurate determination of the critical line of the square ising antiferromagnet in a field several points on the critical line of the simple quadratic antiferromagnetic ising model in a field are located with high precision this is accomplished by means of finite size scaling of the magnetic correlation length of n infinity strips the latter quantities were determined by means of the transfer matrix method for strip widths up to n 20 an expression possibly with the exact form is constructed which reproduces the critical line with an accuracy to the order of 10 10

transfer matrix test of the two cell mean field renormalization group abstract a transfer matrix approach has been worked out to test the predictions of the two cell mean field renormalization group mfrg for the square ising cells with linear size up to l 11 the convergence of the finite size critical couplings towards the exact value both for mfrg and for the cluster mfa is shown and the limit of the ratio yh yt consistent with the corresponding universal value is found applications within mfa are also briefly discussed

simultaneous analysis of several models in the three dimensional ising universality class we investigate several three dimensional lattice models believed to be in the ising universality class by means of monte carlo methods and finite size scaling these models include spin 1 models with nearestneighbor interactions on the simple cubic and on the diamond lattice for the simple cubic lattice we also include models with third neighbor interactions of varying strength and some equivalent neighbor models also included are a spin 1 model and a hard core lattice gas separate analyses of the numerical data confirm the ising like critical behavior of these systems on this basis we analyze all these data simultaneously such that the universal parameters occur only once this leads to an improved accuracy the thermal magnetic and irrelevant exponents are determined as y t51 5868 3 y h52 4816 1 and y i520 821 5 respectively the binder ratio is estimated as q5 m 2 2 m 4 50 62 341 4

two layer fluid formation and propagation of periodic solitons induced by 3 1 dimensional kp equation abstract in this paper multi wave solutions of kadomtsev petviashvili kp equation with time variable coefficient are obtained it is found that the formation of two layer with bright and dark soliton which are symmetric these solitons are transversely periodic as periodic of two soliton and two antisoliton in time with cusps localized in space these two types of waves propagate in an opposite direction relative the higher layer the autonomous behavior may be argued to the fact that the kp is composed of the derivative and the anti derivative terms

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

on closed form solutions of 2 1 breaking soliton system by similarity transformations method abstract in the present research similarity transformation method via lie group theory is proposed to seek some more exact closed form solutions of the 2 1 dimensional breaking soliton system the system describes the interactions of the riemann wave along y axis and long wave along x axis some explicit solutions of breaking soliton system are attained with appropriate choices of the arbitrary functions and making use of arbitrary constants involved in the infinitesimals in order to obtain physically meaningful solutions numerical simulation is performed on the basis of graphical representation the physical analysis of solutions reveals into multi solitons periodic quadratic asymptotic and stationary profiles

breather type soliton and two soliton solutions for modified korteweg de vries equation in this letter different kinds of solutions including breather type soliton and two soliton solutions are obtained for the modified korteweg de vries m kdv equation by using bilinear form the extended homoclinic test approach and dependent variable transformations moreover we point out that the author did not obtain so called periodic two soliton solutions in w long in press 1

critical phenomena of the hard sphere lattice gas on the simple cubic lattice abstract we study the critical phenomena of the hard sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion by the monte carlo method we get the critical exponents v 0 313 9 and v 2 37 2 where is the critical exponent for the staggered density for the staggered compressibility and v for the correlation length

exact three wave solution for higher dimensional kdv type equation a new periodic type of three wave solutions including periodic two solitary solution doubly periodic solitary solution and breather type of two solitary solution for the 1 2 dimensional and 1 3 dimensional kdv type equations are obtained using hirota s bilinear form and generalized three wave type of ansatz approach

volatility distribution in the s p500 stock index abstract we study the volatility of the s p500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log normal function further using detrended fluctuation analysis we show that the volatility is power law correlated with hurst exponent 0 9

varieties of long memory models long memory is defined as a series having a slowly declining correlogram or equivalently an infinite spectrum at zero frequency fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory including generalized fractionally integrated models arising from aggregation time changing coefficient models and possibly nonlinear models it seems that there are many classes of processes that deserve further study the relevance of long memory is illustrated using absolute returns from a daily stock market index

conformal invariance and the ising model on a spheroid we formulate conformal mappings between an infinite plane and a spheroid and one between a semi infinite plane and a half spheroid special cases of the spheroid include the surface of an infinitely long cylinder of a sphere and of a flat disc these mappings are applied to the critical ising model for the case of the sphere and the flat disc we derive analytical expressions for the second and the fourth moments of the magnetization density and thus for the binder cumulant next we investigate ising models on spheroids and half spheroids by means of a continuous cluster monte carlo method for simulations in curved geometries fixed and free boundary conditions are imposed for half spheroids the monte carlo data are analyzed by finite size scaling critical values of the binder cumulants and other ratios on the sphere and on the flat disc agree precisely with the exact calculations mentioned above at criticality we also sample two and one point correlation functions on spheroids on half spheroids respectively the magnetic and temperature scaling dimensions as determined from the monte carlo data and the theory of conformal invariance are in good agreement with exact results

applications of hta and ehta to ytsf equation new approaches homoclinic test approach hta and extended homoclinic test approach ehta are proposed to seek solitary wave solution of high dimensional nonlinear wave system exact periodic solitary wave periodic soliton cross solitary wave and doubly periodic wave solutions for ytsf equation are obtained using hta and ehta respectively

universality in the two dimensional continuous spin model monte carlo methods have been used to analyse the critical behaviour of the d 2 border phi 4 model which according to a recent series expansion study violates expectations based upon universality the results suggest that the model does in fact fall into the ising universality class at least as regards those parameters which characterise the critical point configurations of the ordering variable

universal ratio of magnetization moments in two dimensional ising models the authors calculate the universal critical point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic ising models on the square and on the triangular lattices periodic boundary conditions are used in accordance with the four fold and six fold rotational symmetries of the respective lattices these results which are obtained by means of an analysis of finite size data computed with a transfer matrix technique have an accuracy of the order of one millionth this analysis is also applied to rectangular systems with arbitrary aspect ratios

the simple quadratic ising model with crossing bonds abstract we investigate the ferromagnetic critical line of the simple quadratic ising model with nearest neighbour and next nearest neighbour interactions by means of monte carlo renormalisation group and analytic methods a comparison of the monte carlo results with the renormalisation group trajectories yields the asymptotic behaviour of the critical line in the strong coupling limit a number of figures of spin configurations is included to illustrate the physical behaviour of the model

the breather type and periodic type soliton solutions for the 2 1 dimensional breaking soliton equation exact breather type and periodic type soliton solutions including the double breather type soliton solutions the breather type periodic soliton solutions and breather type two soliton solutions and the periodic type two soliton and three soliton solutions for the 2 1 dimensional breaking soliton equation are obtained using the extended three wave method etm the results show that the etm may provide us with a straightforward and effective mathematical tool for seeking multi wave solutions of higher dimensional nonlinear evolution equations

high dimensional lattice gases we investigate the critical behaviour of hard core lattice gases in four five and six dimensions by means of monte carlo simulations in order to suppress critical slowing down we use a geometrical cluster monte carlo algorithm in particular nearest neighbour exclusion lattice gases on simple hypercubic lattices are investigated these models undergo ising like ordering transitions where the majority of the lattice gas particles settle on one of two sublattices a finite size scaling analysis of the simulation data confirms that these lattice gases display classical critical behaviour the results agree with the renormalization predictions at and above the upper critical dimensionality in particular the predicted value of the binder cumulant is confirmed

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

a monte carlo study of the entropy the pressure and the critical behavior of the hard square lattice gas an approximate technique for estimating the entropys with computer simulation methods suggested recently by meirovitch is applied here to the metropolis monte carlo mc simulation of the hard square lattice gas in both the grand canonical and the canonical ensembles the chemical potential calculated by widom s method ands enable one to obtain also the pressurep the mc results are compared with results obtained with pade approximants pa and are found to be very accurate for example at the critical activityz c the mc and the pa estimates fors deviate by 0 5 beyondz c this deviation decreases to 0 01 and comparable accuracy is detected forp we argue that close toz c our results fors andp are more accurate than the pa estimates independent of the entropy study we also calculate the critical exponents by applying fisher s finite size scaling theory to the results for the long range order the compressibility and the staggered compressibility obtained for several lattices of different size at zc the data are consistent with the critical exponents of the plane ising lattice 1 8 1 7 4 and 0 our values for and agree with series expansion and renormalization group results respectively 0 has been obtained also by matrix method studies it differs however from the estimate of baxteret al 0 09 0 05 as far as we know has not been calculated yet

universality of the ising and the s 1 model on archimedean lattices a monte carlo determination the ising models s 1 2 and s 1 are studied by efficient monte carlo schemes on the 3 4 6 4 and the 3 3 3 3 6 archimedean lattices the algorithms used a hybrid metropolis wolff algorithm and a parallel tempering protocol are briefly described and compared with the simple metropolis algorithm accurate monte carlo data are produced at the exact critical temperatures of the ising model for these lattices their finite size analysis provide with high accuracy all critical exponents which as expected are the same with the well known 2d ising model exact values a detailed finite size scaling analysis of our monte carlo data for the s 1 model on the same lattices provides very clear evidence that this model obeys also very well the 2d ising model critical exponents as a result we find that recent monte carlo simulations and attempts to define effective dimensionality for the s 1 model on these lattices are misleading accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two archimedean lattices

diversity of critical behavior within a universality class we study spatial anisotropy effects on the bulk and finite size critical behavior of the mathrm o n symmetric anisotropic ensuremath varphi 4 lattice model with periodic boundary conditions in a d dimensional hypercubic geometry above at and below t c the absence of two scale factor universality is discussed for the bulk order parameter correlation function the bulk scattering intensity and for several universal bulk amplitude relations the anisotropy parameters are observable by scattering experiments at t c for the confined system renormalization group theory within the minimal subtraction scheme at fixed dimension d for 2ldl4 is employed in contrast to the ensuremath epsilon 4 ensuremath d expansion the fixed d finite size approach keeps the exponential form of the order parameter distribution function unexpanded for the case of cubic symmetry and for n 1 our perturbation approach yields excellent agreement with the monte carlo mc data for the finite size amplitude of the free energy of the three dimensional ising model at t c by mon phys rev lett 54 2671 1985 the ensuremath epsilon expansion result is in less good agreement below t c a minimum of the scaling function of the excess free energy is found we predict a measurable dependence of this minimum on the anisotropy parameters the relative anisotropy effect on the free energy is predicted to be significantly larger than that on the binder cumulant our theory agrees quantitatively with the nonmonotonic dependence of the binder cumulant on the ferromagnetic next nearest neighbor nnn coupling of the two dimensional ising model found by mc simulations of selke and shchur j phys a 38 l739 2005 our theory also predicts a nonmonotonic dependence for small values of the antiferromagnetic nnn coupling and the existence of a lifshitz point at a larger value of this coupling the nonuniversal anisotropy effects in the finite size scaling regime are predicted to satisfy a kind of restricted universality the tails of the large l behavior at t ensuremath ne t c violate both finite size scaling and universality even for isotropic systems as they depend on the bare four point coupling of the ensuremath varphi 4 theory on the cutoff procedure and on subleading long range interactions

universality in two dimensional ising models we have used finite size scaling and transfer matrix techniques to calculate accurately the critical exponents of three two dimensional ising like models for which no exact solution is available two spin 12 models with crossing bonds and a spin 1 model the results for the temperature and magnetic exponents are very close to the exact results for exactly solvable models which are assumed to be in the same universality class differences are between 10 5 and a few times 10 4 and within the apparent numerical uncertainties we also present an estimate of the critical point of the spin 1 model and some preliminary results concerning universal properties of critical amplitudes

the non interacting hard square lattice gas ising universality the critical exponents of the non interacting hard square lattice gas model are determined by means of series analysis and finite size scaling the series analysis leads to results for the exponents that are consistent with the expected ising universal values a scaling analysis is performed on different types of numerical finite size data obtained by means of the transfer matrix method the results support ising universality a procedure based on conformal invariance reproduces the known ising temperature and magnetic exponents within 10 6 furthermore we estimate the critical density of the hard square model as rho c 0 367 743 000 5

on bandlimitedness and lag limitedness of fractional gaussian noise abstract the contributions of this short paper are two fold we shall show two interesting properties of fractional gaussian noise fgn namely its bandlimitedness and lag limitedness the computation formulas for the maximum frequency of bandlimited fgn and the maximum lag of lag limited fgn are proposed in addition we will give a new explanation of the statistical dependences of fgn based on the present bandlimitedness and lag limitedness of fgn