on the elliptic 2 solid on solid model functional relations and determinants in this work we study an elliptic solid on solid model with domain wall boundaries having the elliptic quantum group ep gl2 as its underlying symmetry algebra we elaborate on results previously presented in galleas phys rev e 94 010102 2016 and extend our analysis to include continuous families of single determinantal representations for the model s partition function interestingly our families of representations are parameterized by two continuous complex variables which can be arbitrarily chosen without affecting the partition function in this work we study an elliptic solid on solid model with domain wall boundaries having the elliptic quantum group ep gl2 as its underlying symmetry algebra we elaborate on results previously presented in galleas phys rev e 94 010102 2016 and extend our analysis to include continuous families of single determinantal representations for the model s partition function interestingly our families of representations are parameterized by two continuous complex variables which can be arbitrarily chosen without affecting the partition function

entanglement entropy from corner transfer matrix in forrester baxter non unitary rsos models using a corner transfer matrix approach we compute the bipartite entanglement renyi entropy in the off critical perturbations of non unitary conformal minimal models realised by lattice spin chains hamiltonians related to the forrester baxter rsos models bianchini et al 2015 j stat mech p03010 in regime iii this allows to show on a set of explicit examples that the renyi entropies for non unitary theories rescale near criticality as the logarithm of the correlation length with a coefficient proportional to the effective central charge this complements a similar result recently established for the size rescaling at the critical point bianchini et al 2015 j phys a math theor 48 04ft01 showing the expected agreement of the two behaviours we also compute the first subleading unusual correction to the scaling behaviour showing that it is expressible in terms of expansions of various fractional powers of the correlation length related to the differences between the conformal dimensions of fields in the theory and the minimal conformal dimension finally a few observations on the limit leading to the off critical logarithmic minimal models of pearce and seaton 2012 j stat mech p09014 are put forward

scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

height probabilities in solid on solid models i for pt i see ibid vol 19 p l923 1986 the rsos 3 model is a sequence of two dimensional solid on solid models with integer heights restricted between 1 and r 1 and nearest neighbours differing by 0 1 or 1 it has an exact solution manifold with four regimes of distinct physical behaviour along which the height probabilities in the bulk of the system can be calculated using some results of the previous letter in this series the authors calculate the height probabilities for two of the regimes appropriate order parameters are defined and their critical exponents calculated

precursors of extreme increments we investigate precursors and the predictability of extreme increments in a time series the events we are focusing on consist in large increments within successive time steps we are especially interested in understanding how the quality of the predictions depends on the strategy to choose precursors on the size of the event and on the correlation strength we study the prediction of extreme increments analytically in an autoregressive process of order 1 and numerically in wind speed recordings and long range correlated autoregressive moving average processes data we evaluate the success of predictions via receiver operator characteristics roc curves furthermore we observe an increase of the quality of predictions with increasing event size and with decreasing correlation in all examples both effects can be understood by using the likelihood ratio as a summary index for smooth roc curves

paths and partitions combinatorial descriptions of the parafermionic states the zk parafermionic conformal field theories despite the relative complexity of their modes algebra offer the simplest context for the study of the bases of states and their different combinatorial representations three bases are known the classic one is given by strings of the fundamental parafermionic operators whose sequences of modes are in correspondence with restricted partitions with parts at distance k 1 differing at least by 2 another basis is expressed in terms of the ordered modes of the k 1 different parafermionic fields which are in correspondence with the so called multiple partitions both types of partitions have a natural bressoud path representation finally a third basis formulated in terms of different paths is inherited from the solution of the restricted solid on solid model of andrews baxter forrester the aim of this work is to review in a unified and pedagogical exposition these four different combinatorial representations of the states of the zk parafermionic models

a monomial basis for the virasoro minimal series m p p the case 1 p p 2 quadratic relations are given explicitly in two cases of chiral conformal field theory and monomial bases of the representation spaces are constructed by using the fourier components of the intertwiners the first case is the 2 1 primary fields for the p p minimal series m r s 1 r p 1 1 s p 1 for the virasoro algebra where 1 p p 2 we restrict ourselves to the case p 3 for which the 2 1 primary field exists the second case is the intertwiners corresponding to the two dimensional representation for the level k integrable highest weight modules v 0 k for the affine lie algebra open image in new window

exact solubility of the self dual and the string melting points in the restricted solid on solid model the restricted solid on solid model which describes the roughening of two dimensional interfaces is found to be exactly soluble in two instances at a point where the model is self dual under the duality transformation of the five state clock model and at the string melting transition where the model belongs to the same universality class as an ising model on a transverse vibrating lattice both points are located in the subspace of the 19 vertex model solved by zamolodchikov and fateev 1980

effect of nonlinear correlations on the statistics of return intervals in multifractal data sets we study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations we find that nonlinear correlations in the record lead to a power law i decay of the autocorrelation function of the return intervals ii increase in the conditional return period and iii decay in the probability density function of the return intervals we show explicitly that all the observed quantities depend both on the threshold value and system size and hence there is no simple scaling observed we also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation

indication of multiscaling in the volatility return intervals of stock markets a certain trend with the mean interval we generate surrogate records using the schreiber method and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law we also find that the original and surrogate records exhibit slight tendencies for short and long due to the discreteness and finite size effects of the records respectively to avoid as possible those effects for testing the multiscaling behavior we investigate the moments in the range 10100 and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks the distribution of for the surrogate records are very narrow and centered around 0 this suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility

integrable boundaries conformal boundary conditions and a d e fusion rules the sl 2 minimal theories are classified by a lie algebra pair where g is of a d e type for these theories on a cylinder we propose a complete set of conformal boundary conditions labelled by the nodes of the tensor product graph the cylinder partition functions are given by fusion rules arising from the graph fusion algebra of we further conjecture that for each conformal boundary condition an integrable boundary condition exists as a solution of the boundary yang baxter equation for the associated lattice model the theory is illustrated using the or three state potts model

influence of the event magnitude on the predictability of an extreme event we investigate the predictability of extreme events in time series the focus of this work is to understand under which circumstances large events are better predictable than smaller events therefore we use a simple prediction algorithm based on precursory structures which are identified using the maximum likelihood principle using the receiver operator characteristic curve as a measure for the quality of predictions we find that the dependence on the event size is closely linked to the probability distribution function of the underlying stochastic process we evaluate this dependence on the probability distribution function analytically and numerically if we assume that the optimal precursory structures are used to make the predictions we find that large increments are better predictable if the underlying stochastic process has a gaussian probability distribution function whereas larger increments are harder to predict if the underlying probability distribution function has a power law tail in the case of an exponential distribution function we find no significant dependence on the event size furthermore we compare these results with predictions of increments in correlated data namely velocity increments of a free jet flow the velocity increments in the free jet flow are in dependence on the time scale either asymptotically gaussian or asymptotically exponential distributed the numerical results for predictions within free jet data are in good agreement with the previous analytical considerations for random numbers

exact calculation of the local height probabilities in the body centred sos model the local height probabilities pa and the mean square height average h2 are calculated exactly for the smooth phase of the body centred solid on solid model near criticality pa approximately k t 1 4 and h2 approximately k t 1 2 where t is the deviation from criticality parameter and k k are constants specified in the text

q trinomial identities we obtain connection coefficients between q binomial and q trinomial coefficients using these one can transform q binomial identities into q trinomial identities and back again to demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of berkovich mccoy and pearce which have recently arisen in their study of the 2 1 and 1 5 perturbations of minimal conformal field theory

scattering from a periodic array of free standing arbitrarily shaped perfectly conducting or resistive patches a fast fourier transform fft based iterative approach for computing the fields scattered by an infinite array of free standing patches is presented the method is capable of handling patches that are lossy and have arbitrary shape it is useful for analyzing configurations that may not have been analyzed previously though a rectangular fft is used the formulation allows the study of the common triangular array periodicities results for various geometries are presented and are compared with existing results

solvable models in statistical mechanics from onsager onward there is now a whole field in mathematical physics concerned with solvable models in statistical mechanics field theory and related areas we indicate the influence that onsager s solution of the planar ising model has had and continues to have on this field

bistatic scattering from a three dimensional object over a randomly rough surface using the fdtd algorithm a numerical finite difference time domain approach for electromagnetic scattering from an object over a randomly rough surface in three dimensional 3 d model is developed rough surface is truncated in numerical simulation by using the periodic surface extension and one period of the rough surface with dependence of the correlation length is used for scattering computation generation of the incident wave upon the rough surface is presented a numerical model and algorithm of a single object on or above a rough surface are developed polarized bistatic scattering from the object and rough surface is obtained based on numerical distribution of the near zone fields comparison with conventional two dimensional model is also discussed

further exact solutions of the eight vertex sos model and generalizations of the rogers ramanujan identities the restricted eight vertex solid on solid sos model is an exactly solvable class of two dimensional lattice models to each sitei of the lattice there is associated an integer heightli restricted to the range 1 li r 1 the boltzmann weights of the model are expressed in terms of elliptic functions of period 2k and involve a parameter in an earlier paper we considered the case k r here we generalize those considerations to the case sk r s an integer relatively prime tor we are again led to generalizations of the rogers ramanujan identities

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

critical correlations in a z invariant inhomogeneous ising model abstract we study the critical spin spin correlation function in the z invariant inhomogeneous ising model which includes the rectangular triangular honeycomb and checkerboard lattices as special cases using quadratic difference equations we derive various explicit representations for the correlation function confirming and simplifying also a miraculous result of baxter

application of aim and mbpe techniques to accelerate modeling of 3 d doubly periodic structures with nonorthogonal lattices composed of bianisotropic media an efficient methodology is introduced for rapid analysis and design of three dimensional 3 d doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral febi methods the 3 d doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily shaped metallic patches based on floquet theory and periodic boundary conditions the original stated problem that involves infinite periodic structures can be converted into a single unit cell using the equivalence principle the derived bi equation formulation is applied to the top and bottom surfaces of the unit cell which results in a perfectly reflectionless boundary condition for the fe based approach then the unit cell was meshed using triangular prismatic volume elements which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction the adaptive integral method aim was employed to accelerate the calculation of the matrix vector product for the bi portion within the iterative solver furthermore a model based parameter estimation mbpe technique was proposed for the wide band interpolation of the required impedance matrix elements in the bi part for near field components that were used in the aim procedure the accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results e g in comparison with analytical solutions several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily shaped metallic patches bianisotropic materials and nonorthogonal lattice configurations

scaling properties and universality of first passage time probabilities in financial markets financial markets provide an ideal frame for the study of crossing or first passage time events of non gaussian correlated dynamics mainly because large data sets are available tick by tick data of six futures markets are herein considered resulting in fat tailed first passage time probabilities the scaling of the return with its standard deviation collapses the probabilities of all markets examined and also for different time horizons into single curves suggesting that first passage statistics is market independent at least for high frequency data on the other hand a very closely related quantity the survival probability shows away from the center and tails of the distribution a hyperbolic t ensuremath 1 2 decay typical of a markovian dynamics albeit the existence of memory in markets modifications of the weibull and student distributions are good candidates for the phenomenological description of first passage time properties under certain regimes the scaling strategies shown may be useful for risk control and algorithmic trading

quantifying the range of cross correlated fluctuations using a q l dependent ahxa coefficient abstract recently based on analogous height cross correlation analysis ahxa a cross correlation coefficient l has been proposed to quantify the levels of cross correlation on different temporal scales for bivariate series a limitation of this coefficient is that it cannot capture the full information of cross correlations on amplitude of fluctuations in fact it only detects the cross correlation at a specific order fluctuation which might neglect some important information inherited from other order fluctuations to overcome this disadvantage in this work based on the scaling of the q th order covariance and time delay l we define a two parameter dependent cross correlation coefficient q l to detect and quantify the range and level of cross correlations this new version of q l coefficient leads to the formation of a q l surface which not only is able to quantify the level of cross correlations but also allows us to identify the range of fluctuation amplitudes that are correlated in two given signals applications to the classical arfima models and the binomial multifractal series illustrate the feasibility of this new coefficient q l in addition a statistical test is proposed to quantify the existence of cross correlations between two given series applying our method to the real life empirical data from the 1999 2000 california electricity market we find that the california power crisis in 2000 destroys the cross correlation between the price and the load series but does not affect the correlation of the load series during and before the crisis

an adi fdtd method for periodic structures in this communication the alternating direction implicit finite difference time domain adi fdtd method is extended to analyze periodic structures in the implicit updates of the adi fdtd method the periodic boundary condition leads to a cyclic matrix instead of inverting the cyclic matrix directly the problem is converted into two auxiliary linear systems that can be solved using the tridiagonal matrix solver consequently only 7n arithmetic operations are required for each implicit update and the efficiency of the adi fdtd method is retained numerical examples further demonstrate the effectiveness of this periodic adi fdtd method

particles in rsos paths we introduce a new representation of the paths of the forrester baxter restricted solid on solid rsos models which represents the states of the irreducible modules of the minimal models this representation is obtained by transforming the rsos paths for the cases p 2p 1 to new paths for which horizontal edges are allowed at certain heights these new paths are much simpler in that their weight is nothing but the sum of the position of the peaks this description paves the way for the interpretation of the rsos paths in terms of fermi type charged particles out of which the fermionic characters could be obtained constructively the derivation of the fermionic character for p 2 and p kp 1 is outlined finally the particles of the rsos paths are put in relation to the kinks and the breathers of the restricted sine gordon model

predictability of critical transitions critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages from bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations the consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition however especially in the presence of noise it is not clear whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions in this contribution we investigate the predictability of critical transitions in conceptual models we study the quadratic integrate and fire model and the van der pol model under the influence of external noise we focus especially on the statistical analysis of the success of predictions and the overall predictability of the system the performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it furthermore we study the influence of the magnitude of transitions on the predictive performance

integral equation modeling of multilayered doubly periodic lossy structures using periodic boundary condition and a connection scheme this paper presents a boundary integral formulation to analyze multilayered doubly periodic lossy structures with arbitrary geometry the formulation is based on the moment method using first order triangular patch basis functions each individual layer is analyzed separately using the simple free space green s function after discretization periodic boundary conditions are imposed on each region and a connection scheme is used to connect the regions metallic patches between layers or on the periodic boundary are also included in the model several examples are presented showing both the flexibility and the accuracy of the method

a nonlocal operator basis from the path representation of the cal m k 1 hbox k 2 and the cal m k 1 hbox 2k 3 minimal models we reinterpret a path describing a state in an irreducible module of the unitary minimal model in terms of a string of charged operators acting on the module s ground state path each such operator acts non locally on a path the path characteristics are then translated into a set of conditions on sequences of operators that provide an operator basis as an application we re derive the vacuum finite fermionic character by constructing the generating function of these basis states these results generalize directly to the models the close relatives of the unitary models in terms of path description

theory of earthquakes interevent times applied to financial markets abstract we analyze the probability density function pdf of waiting times between financial loss exceedances the empirical pdfs are fitted with the self excited hawkes conditional poisson process with a long power law memory kernel the hawkes process is the simplest extension of the poisson process that takes into account how past events influence the occurrence of future events by analyzing the empirical data for 15 different financial assets we show that the formalism of the hawkes process used for earthquakes can successfully model the pdf of interevent times between successive market losses

unconditionally stable fdtd method based on lod scheme for analysis of 2 d periodic structures for modeling periodic structures at oblique incidence an unconditionally stable finite difference time domain technique is presented by applying the locally one dimensional lod scheme to the field transformation technique by splitting the space operator matrix in an appropriate way the transformed maxwell s equations can be subdivided into two sub steps for an efficient implementation the accuracy and efficiency of the proposed method are verified by comparing with the results of the reference 4 and the split field method respectively

efficient implementation of 2 d split field fdtd method for analyzing periodic structures this communication presents an efficient implementation of the 2 d split field method for solving problems of the oblique incident plane wave on periodic structures first by only splitting one field quantity q x and adopting the locally one dimensional scheme the transformed maxwell s equations are reformulated into a concise form and then by some matrix operation the field updating of the proposed method is implemented in the explicit scheme compared with the traditional split field method the courant friedrich levy stability condition of the proposed method is weaker and the cpu time and memory are saved numerical results demonstrate that the proposed method is more efficient

graphical approach to the nonintersecting string model star triangle equation inversion relation and exact solution abstract a general q state nonintersecting string model for q 2 is studied and solved using a graphical approach this model of which special cases were first introduced by strogonov and schultz has recently drawn further attention because of its relation to potts models in its simplest version a uniform separable nonintersecting string model on a quadratic lattice it corresponds to a q2 state potts model with potts spins on every other lattice face we first formulate the related star triangle equation which we solve in terms of a line variable parametrization such a parametrization of a solution of the star triangle equation leads to a simple and direct graphical derivation of an inversion relation for the partition function our graphical analysis also shows that the inversion relation holds if certain boundary effects can be neglected as we shall give a special finite lattice from which the inversion relation can be read off immediately this relation is next solved under appropriate analyticity assumptions again using a simple and direct approach and the result is applied to obtain exact solutions for specific string models

improved risk estimation in multifractal records application to the value at risk in finance we suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above below a certain threshold q and is particularly suited for multifractal records the method is based on the knowledge of the probability w q t ensuremath delta t that within the next ensuremath delta t units of time at least one event above q occurs if the last event occurred t time units ago we propose an analytical estimate of w q and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis which requires considerable fine tuning and is difficult to implement we also show that the estimation of the value at risk which is a standard tool in finances can be improved considerably by the method

entanglement entropy of non unitary conformal field theory here we show that the renyi entanglement entropy of a region of large size l in a one dimensional critical model whose ground state breaks conformal invariance such as in those described by non unitary conformal field theories behaves as ceff n 1 2n log l where ceff c 24delta 0 is the effective central charge c which may be negative is the central charge of the conformal field theory and delta 0 is the lowest holomorphic conformal dimension in the theory we also obtain results for models with boundaries and with a large but finite correlation length and we show that if the lowest conformal eigenspace is logarithmic then there is an additional term proportional to log log l these results generalize the well known expressions for unitary models we provide a general proof and report on numerical evidence for a non unitary spin chain and an analytical computation using the corner transfer matrix method for a non unitary lattice model we use a new algebraic technique for studying the branching that arises within the replica approach and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non unitary models

volatility a hidden markov process in financial time series volatility characterizes the amplitude of price return fluctuations it is a central magnitude in finance closely related to the risk of holding a certain asset despite its popularity on trading floors volatility is unobservable and only the price is known diffusion theory has many common points with the research on volatility the key of the analogy being that volatility is a time dependent diffusion coefficient of the random walk for the price return we present a formal procedure to extract volatility from price data by assuming that it is described by a hidden markov process which together with the price forms a two dimensional diffusion process we derive a maximum likelihood estimate of the volatility path valid for a wide class of two dimensional diffusion processes the choice of the exponential ornstein uhlenbeck expou stochastic volatility model performs remarkably well in inferring the hidden state of volatility the formalism is applied to the dow jones index the main results are that i the distribution of estimated volatility is lognormal which is consistent with the expou model ii the estimated volatility is related to trading volume by a power law of the form sigma proportional variant v0 55 and iii future returns are proportional to the current volatility which suggests some degree of predictability for the size of future returns

fdtd analysis of periodic structures with arbitrary skewed grid an efficient finite difference time domain fdtd algorithm with a simple periodic boundary condition pbc is developed to analyze general periodic structures with arbitrary skewed grids the algorithm is easy to implement and efficient in both memory usage and computation time the stability criterion of the algorithm is angle independent and therefore it is suitable for implementing incidence with angle close to grazing as well as normal incidence the validity of this algorithm is verified through several numerical examples such as dipole and jerusalem cross frequency selective surfaces fss with various skew angles

infinite phased array analysis using fdtd periodic boundary conditions pulse scanning in oblique directions unit cell analysis of infinite phased arrays in the finite difference time domain fdtd is performed by implementation of periodic boundary conditions the technique allows for pulse excitation and oblique scan directions in both the cardinal and intercardinal planes to our knowledge this is the first paper presenting fdtd computations for intercardinal pulse scanning in oblique directions the ordinary yee lattice is used which makes the algorithm easy to incorporate in an already existing fdtd code nonperiodic boundaries are truncated by berenger s see j comput phys vol 127 p 363 79 1996 perfectly matched layer pml active impedance of an infinite dipole array is calculated with the new method and validation is performed via the element by element approach i e by a conventional fdtd simulation of a corresponding large finite array excellent agreement is found and the technique has been numerically stable in all cases analyzed

a three dimensional time domain finite element formulation for periodic structures a formulation is presented for a three dimensional time domain finite element method that can be used to analyze the scattering of a plane wave obliquely incident on a doubly infinite periodic structure using one unit cell a broadband frequency response can be obtained in a single execution the specifics of the method are shown for scattering problems but it should be straightforward to extend it to radiation problems the method solves for a transformed field variable instead of solving directly for the electric field in order to easily enable periodic boundary conditions in the time domain the accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions accurate results are obtained when the excitation frequency range and the geometry are such that no higher order propagating floquet modes are present the accuracy is degraded in the presence of higher order propagating modes due to the rather simple absorbing boundary condition that is used with the present formulation the method is found to be stable even for angles of incidence close to grazing

fdtd analysis of phased array antennas this work presents a new application of the finite difference time domain fdtd method to the generalized analysis of phased array antennas the generality of the fdtd method brings important advantages to the phased array antenna analysis problem allowing the modeling of complex conductor and dielectric geometries with relative ease additionally a new broad band fdtd periodic boundary condition is developed which allows the array problem to be simplified to a periodic unit cell computational domain this hybrid frequency time domain periodic boundary condition enables solution of the periodic phased array problem for arbitrary scan conditions in a broadband fashion the new method is applied to waveguide and stacked microstrip antenna arrays and the numerical results are compared to experimental or analytic solutions demonstrating the validity and utility of this method

performance of multifractal detrended fluctuation analysis on short time series the performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono and multifractal models the reconstruction of the generalized hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series as an application the series of the daily exchange rate between the us dollar and the euro is studied sets with known fractal and multifractal behavior the results are applied to the analysis of the daily exchange rate between the us dollar and the euro this time se ries is relatively short around 3500 entries given that the euro currency debuted at the beginning of 1999 further more in its short life the euro has gone through a dubita tive start followed by a strong couple of years and since around 2008 it has been immersed in a crisis which has threatened its existence this turbulent history makes it interesting to ask if its dynamics have changed with time the paper is organized as follows in the next section the mfdfa method is briefly described and the notation used in the rest of the paper is introduced section iii presents the analysis of the mono and multifractal syn thetic data section iv discusses the application of the results to a time series from finance namely the daily ex change rate between the us dollar and the euro finally the conclusions of this work are presented in section v

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

from path representations to global morphisms for a class of minimal models we construct global observable algebras and global dhr morphisms for the virasoro minimal models with central charge c 2 q q odd to this end we pass from the irreducible highest weight modules to path representations which involve fusion graphs of the c 2 q models the paths have an interpretation in terms of quasi particles which capture some structure of non conformal perturbations of the c 2 q models the path algebras associated to the path spaces serve as algebras of bounded observables global morphisms which implement the superselection sectors are constructed using quantum symmetries we argue that there is a canonical semi simple quantum symmetry algebra for each quasi rational cft in particular for the c 2 q models these symmetry algebras act naturally on the path spaces which allows to define a global field algebra and covariant multiplets therein

further solutions of critical abf rsos models the restricted sos model of andrews baxter and forrester 1984 has been studied the finite size corrections to the eigenvalue spectra of the transfer matrix of the model with a more general crossing parameter have been calculated therefore the conformal weights and the central charges of the non unitary or unitary minimal conformal field have been extracted from the finite size corrections

implementation of the periodic boundary condition in the finite difference time domain algorithm for fss structures a method for implementing the general floquet boundary condition in the finite difference time domain algorithm fdtd is presented the floquet type of phase shift boundary condition is incorporated into the time domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step with this approach the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence theoretical results are compared for various planar frequency selective surfaces fss and for one with a three dimensional element e g a thick double concentric square loop

integral equation modeling of doubly periodic structures with an efficient pmchwt formulation a surface integral equation modeling is described for complex doubly periodic structures to avoid long computations of the slowly convergent pseudoperiodic green s function fictitious surfaces between translated unit cells are set in order to bound regions of the structure within the symmetry cell and use the free space green s function the integral operators on top and bottom surfaces are computed with an algorithm originally used for planar frequency selective surfaces this approach uses a unique periodic pmchwt formulation in all the regions with two different kinds of green s function the method and its advantages are illustrated by two cases in the near ir domain and in the radar domain a frequency selective structure is studied that shows a large flat top bandwidth under oblique incidence and tm polarization

the emerging role of number theory in exactly solvable models in lattice statistical mechanics abstract we review the baxter model the hard hexagon model and their multistate generalizations from a point of view that stresses the connection with modular functions and additive number theory it is shown for example that various physical quantities in the hard hexagon model are all expressible in terms of modular functions the use of rogers ramanujan type identities in solvable models is also reviewed

finite difference time domain modeling of frequency selective surfaces using impedance sheet conditions novel finite difference time domain fdtd models of frequency selective surfaces fss based on impedance sheet conditions are developed the analytical basis of the models lies in impedance sheet conditions with general reactive grid impedances applying to a great variety of grid realizations new models for periodic arrays of metal particles and for the complementary structures of slots in metal screen are formulated for fdtd in the case of normal incidence the properties of the fss are included in the grid impedance which is implemented into fdtd considerably simplifying the otherwise extremely cumbersome modeling task the convergence and the accuracy of the models are assessed with numerical simulations by comparing with analytical and measured reference results

the spin 1 heisenberg chain with uniaxial anisotropy and its classical counterpart abstract the spin 1 heisenberg chain with uniaxial anisotropy is related to a two dimensional roughening model with anisotropic next nearest neighbor interactions using this relation some peculiar features of the phase diagram of the quantum chain can be explained naturally and predictions for the critical exponents are also obtained which agree with previous finite size scaling studies of the quantum model a numerical transfer matrix calculation of the free energy of the roughening model on infinite strips of small width n 6 yields a critical behavior consistent with the one found for the t 0 properties of the quantum chain

efficient calculation of the dispersion diagram of planar electromagnetic band gap structures by the mom bi rme method the characterization of planar electromagnetic band gap structures requires the calculation of the dispersion diagram of the modes supported by the periodic structure and the phase of the reflection coefficient under plane wave illumination we present a novel method for the calculation of the dispersion diagram the electromagnetic analysis is based on the method of moments boundary integral resonant mode expansion mom bi rme method and leads to the formulation of a homogeneous matrix problem the solution of this problem is performed by an iterative procedure for a given value of the propagation phase constant the frequency range is scanned to find the frequencies where the field equation has a nontrivial solution the search of these frequencies is based on the tracking of the eigenvalues in the complex plane and proved more efficient than other classical methods direct search of the determinant zeros singular value decomposition the reflection coefficient can be readily determined by using the mom bi rme method already developed for the analysis of the scattering from frequency selective surfaces the method is applied to the characterization of the classical uniplanar compact photonic bandgap structure and analysis results show the accuracy of the method its efficiency and its convergence properties

the analysis of periodic structures with 2 d staggered grid by fdtd algorithm according to the characteristics of the periodic structures with 2 d staggered grids two new effective construction methods dealing with periodic boundaries based on the finite difference time domain fdtd algorithm are developed in this work the two proposed staggered periodic boundary conditions pbc arrangement methods can be implemented combining the existing boundary data mapping techniques applying these arrangements coordinate change and additional ladder boundary grids can be avoided during the modeling process so that the simulation accuracy of the fdtd algorithm can be maintained the performance and the applicable conditions of the two staggered pbc arrangement methods are discussed and compared with the common nonstaggered pbc arrangement method the validity of the two staggered pbc arrangement methods is verified through the numerical examples of an infinite dielectric slab and jerusalem cross frequency selective surface with 2 d staggered girds

polynomial identities indices and duality for the n 1 superconformal model sm 2 4v we prove polynomial identities for then 1 superconformal modelsm 2 4v which generalize and extend the known fermi bose character identities our proof uses theq trinomial coefficients of andrews and baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq series on the fermionic side we use these polynomials to demonstrate a dual relation underq q 1 betweensm 2 4v andm 2v 1 4v we also introduce a genralization of the witten index which is expressible in terms of the rogers false theta functions

boundary conformal field theories and loop models we propose a systematic method to extract conformal loop models for rational conformal field theories cft the method is based on defining an ade model for boundary primary operators by using the fusion matrices of these operators as adjacency matrices these loop models respect the conformal boundary conditions we discuss the loop models that can be extracted by this method for minimal cfts and then we give dilute o n loop models on the square lattice as examples for these loop models we also give some proposals for wzw su 2 models

spectral fdtd a novel technique for the analysis of oblique incident plane wave on periodic structures this paper introduces a new technique which calculates the reflection coefficient for the plane wave incident on planar periodic structures the method referred to as spectral finite difference time domain sfdtd replaces the conventional single angle incident wave with a constant transverse wavenumber ctw wave because the transverse wavenumbers are constant the fields have no delay in the transverse plane x y plane and pbc periodic boundary condition can be directly implemented in the time domain for both oblique and normal incident waves the stability criterion for this new fdtd technique is angle independent and therefore this method works well for incident angles close to grazing spl theta 90 spl deg as well as normal incident spl theta 0 spl deg this shows the efficiency of the method compared to other available fdtd techniques for the same purpose that force a more restricted stability criterion as angles turns to grazing the validity of this method is verified by comparing the reflection coefficient calculated by this method with the analytical results of a grounded slab the results of this technique are also compared with method of moments for a periodic array of metallic patches and a good agreement is observed a periodic array of metallic patches above a pec plate is analyzed and the reflection coefficient is calculated over a wide frequency band for angles varying from 0 spl deg to close to 90 spl deg

local height probabilities in a composite andrews baxter forrester model we study the local height probabilities in a composite height model derived from the restricted solid on solid model introduced by andrews baxter and forrester and their connection with conformal field theory characters the obtained conformal field theories also describe the critical behavior of the model at two different critical points in addition at criticality the model is equivalent to a one dimensional chain of anyons subject to competing two and three body interactions the anyonic chain interpretation provided the original motivation to introduce the composite height model and by obtaining the critical behavior of the composite height model the critical behavior of the anyonic chains is established as well depending on the overall sign of the hamiltonian this critical behavior is described by a diagonal coset model generalizing the minimal models for one sign and by fateev zamolodchikov parafermions for the other

memory effects in the statistics of interoccurrence times between large returns in financial records we study the statistics of the interoccurrence times between events above some threshold q in two kinds of multifractal data sets multiplicative random cascades and multifractal random walks with vanishing linear correlations we show that in both data sets the relevant quantities probability density functions and the autocorrelation function of the interoccurrence times as well as the conditional return period are governed by power laws with exponents that depend explicitly on the considered threshold by studying a large number of representative financial records market indices stock prices exchange rates and commodities we show explicitly that the interoccurrence times between large daily returns follow the same behavior in a nearly quantitative manner we conclude that this kind of behavior is a general consequence of the nonlinear memory inherent in the multifractal data sets

3d weakly conditionally stable fdtd method for analyzing periodic structures by dividing the 3d transformed maxwell s equations into two parts and applying the crank nicolson cn scheme to each part four substep implicit procedures are obtained after adjusting the order of four substeps a weakly conditionally stable finite difference time domain wcsfdtd method is derived for solving the 3d problems of oblique incident plane wave on periodic structures this method is very suitable for analyzing the problems which have fine structures in one or two directions and the courant friedrich levy cfl stability condition of it is more relaxed than that of the original held transformation methods numerical examples demonstrate that the presented technology is more efficient especially at the high incident angle

the baxter revolution i review the revolutionary impact rodney baxter has had on statistical mechanics beginning with his solution of the 8 vertex model in 1971 and the invention of corner transfer matrices in 1976 to the creation of the rsos models in 1984 and his continuing current work on the chiral potts model