higher order correlations of tchebyscheff maps we determine the higher order correlation functions of iterates of tchebyscheff polynomials of arbitrary order n the non vanishing correlations can be described by suitable sets of graphs these graphs allow for a perturbative evaluation of invariant densities for langevin like systems that are driven by deterministic chaotic forces generated by tchebyscheff maps rather than gaussian white noise

approach to gaussian stochastic behavior for systems driven by deterministic chaotic forces we consider skew product dynamical systems that describe the stroboscopic dynamics of a damped particle subjected to a chaotic kick force in a suitable scaling limit the dynamics converges to the ornstein uhlenbeck process we investigate the deterministic chaotic corrections in the vicinity of this gaussian limit case for various examples of chaotic forces we present numerical evidence that for certain classes of chaotic forces the deterministic chaotic corrections of the invariant density are universal we provide analytical results for forces generated by tchebyscheff maps and sketch a renormalization group theory in the space of probability densities

chaotic resonance two state model with chaos induced escape over potential barrier we consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation we derive analytical expressions of chaos induced transition rate between the neighboring potential wells based on the inhomogeneous smoluchowski equation our first order analysis reveals that the transition rate has the form of the kramers escape rate except for a perturbed prefactor this modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise by means of the two state model and the chaos induced transition rate we arrive at an analytical expression of the signal to noise ratio snr our first order snr shows that chaotic resonance can correspond directly to stochastic resonance

application of generalized thermostatistics to fully developed turbulence abstract we apply the formalism of non extensive statistical mechanics to fully developed turbulent flows we obtain analytical formulas for probability density functions of velocity differences depending on distance r and reynolds number r which are in very good agreement with turbulence experiments the skewness is taken into account by analysing universal contributions due to higher order correlations of the chaotic dynamics we also calculate the moment scaling exponents m which also agree well with experimental data

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

a model based parameter estimation technique for wide band interpolation of periodic moment method impedance matrices with application to genetic algorithm optimization of frequency selective surfaces a model based parameter estimation mbpe technique is introduced in this paper for efficiently interpolating periodic moment method pmm impedance matrices over a wide frequency band in the model only the floquet harmonics that strongly affect the frequency band of interest are employed to approximate the matrix elements while the contributions from all other higher order harmonics are compactly represented by two additional terms the derivation of the model is physics based and the objective is to find the coefficients of the terms in the model by utilizing the values of the impedance matrix elements calculated via pmm at only a few frequency points the number and position of these fitting points can be pre determined from the cutoff frequencies of the floquet harmonics which allows the mbpe interpolation process in this case to be completely automated in other words the number and position of the sampling points are only dictated by the periodicity of the frequency selective surface fss structure and the frequency range of interest unlike many of the other scattering parameter based techniques the shape and the resonances in the response of the fss do not have any impact on the construction of the interpolation model this makes it particularly useful in genetic algorithm ga aided fss design since for a fixed periodicity and frequency range the mbpe interpolation is independent of the scattering response of candidate fss designs several examples of the new pmm mbpe approach are presented including one in which it is used to considerably speed up the ga based design process for a reconfigurable fss

one dimensional dynamics for traveling fronts in coupled map lattices multistable coupled map lattices typically support traveling fronts separating two adjacent stable phases we show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one dimensional circle homeomorphism whose rotation number gives the propagation velocity the mode locking of the velocity with respect to the system parameters then typically follows we study the behavior of fronts near the boundary of parametric stability and we explain how the mode locking tends to disappear as we approach the continuum limit of an infinite density of sites

chaotic cascade model for turbulent velocity distributions a coupled map lattice is introduced that simulates the time evolution of velocity differences in fully developed turbulent flows the model considered is an extension of the langevin theory to chaotic driving forces acting on a self similar cascade of spatial levels compared to full simulations of the navier stokes equation the amount of necessary computing time is negligible despite its simplicity the model is in perfect agreement with experimentally observed results provided the chaotic driving force is generated by the fully developed logistic map with parameter value ensuremath mu 2 the shape of the velocity distributions the slight asymmetry the stretched exponential tails as well as the moment scaling exponents mathrm ensuremath zeta mathit m come out in precisely the same way as in experimental measurements of high reynolds number flows

quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series we describe methods of estimating the entire lyapunov spectrum of a spatially extended system from multivariate time series observations provided that the coupling in the system is short range the jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions this circumvents the curse of dimensionality that prevents the accurate reconstruction of high dimensional dynamics from observed time series the technique is illustrated using coupled map lattices as prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying

the model based parameter estimation of antenna radiation patterns using windowed interpolation and spherical harmonics techniques previously reported for interpolating antenna radiation patterns simultaneously in both the spatial and frequency domains are reexamined here in order to develop new algorithms with improved efficiency and speed while maintaining comparable accuracy to this end interpolation in the frequency domain is constrained to a windowed scheme whereby a series of reduced order pade spl acute rational function fitting models of only three or four sampling frequencies are used to interpolate over a relatively large bandwidth the use of this piece wise technique is shown to reduce the complexity of determining the unknown coefficients without any significant loss in the resulting interpolation accuracy or increase in the required number of sampling frequencies in this paper exact analytical expressions are found for the unknown coefficients that allow the spatial domain interpolation to be performed entirely separate from the frequency domain interpolation the technique is applied to the case of a 0 5 meter dipole modeled from 150 to 950 mhz and for spl theta from 0 spl deg to 90 spl deg using fitting windows with three and four sampling frequencies the results are compared to those obtained using a previously developed generalized simultaneous interpolation procedure in the spatial domain spherical harmonics are introduced as model based fitting functions for antenna radiation patterns specifically interpolation procedures are developed using zonal harmonics and tesseral harmonics to model one and two dimensional far field radiation patterns respectively the case of a z oriented 0 5 meter dipole is considered to demonstrate the efficiency and accuracy obtained by applying these physically based fitting models in the spatial domain zonal harmonics are used to interpolate far field radiation patterns of this antenna for spl theta from 0 spl deg to 180 spl deg for several different frequencies over the range from 150 to 950 mhz this example demonstrates the attractiveness of using spherical harmonics functions to accurately and efficiently interpolate radiation patterns in the spatial domain

transition from lognormal to χ2 superstatistics for financial time series abstract share price returns on different time scales can be well modelled by a superstatistical dynamics here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales it is shown that while 2 superstatistics works well on a time scale of days on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics the system dynamics thus exhibits a transition from lognormal to 2 superstatistics as a function of time scale we discuss a more general model interpolating between both statistics which fits the observed data very well we also present results on correlation functions of the extracted superstatistical volatility parameter which exhibits exponential decay for returns on large time scales whereas for returns on small time scales there are long range correlations and power law decay

the simultaneous interpolation of antenna radiation patterns in both the spatial and frequency domains using model based parameter estimation the pade rational function fitting model commonly used for model based parameter estimation mbpe in the frequency domain is enhanced to include spatial dependence in the numerator and denominator coefficients this allows the function to interpolate an antenna radiated electric field pattern in both the frequency and spatial domains simultaneously such that a single set of coefficients can be used to accurately reconstruct an entire radiation pattern at any frequency in the fitting model range a simple procedure is introduced for transforming interpolated electric fields into gain patterns using input impedance versus frequency curves also obtained via mbpe the utility of this method is demonstrated by applying it to a dipole antenna over a frequency range of 150 950 mhz and using a polynomial representation in spl theta for the coefficient spatial dependence it is also used to estimate radiation patterns for a three element yagi array between the frequencies of 470 and 500 mhz using a binomial representation for the spatial variation that includes terms dependent on spl theta as well as spl phi the use of this method for interpolating radiation patterns has at least two significant advantages one being large compression ratios for the amount of data that must be stored to accurately reproduce patterns and the other being a significant decrease in the amount of time required for modeling problems with large computational domains

from the perron frobenius equation to the fokker planck equation we show that for certain classes of deterministic dynamical systems the perron frobenius equation reduces to the fokker planck equation in an appropriate scaling limit by perturbative expansion in a small time scale parameter we also derive the equations that are obeyed by the first and second order correction terms to the fokker planck limit case in general these equations describe non gaussian corrections to a langevin dynamics due to an underlying deterministic chaotic dynamics for double symmetric maps the first order correction term turns out to satisfy a kind of inhomogeneous fokker planck equation with a source term for a special example we are able solve the first and second order equations explicitly

non equilibrium statistical mechanics of turbulence the macroscopic study of hydrodynamic turbulence is equivalent at an abstract level to the microscopic study of a heat flow for a suitable mechanical system ruelle pnas 109 20344 20346 2012 turbulent fluctuations intermittency then correspond to thermal fluctuations and this allows to estimate the exponents tau p and zeta p associated with moments of dissipation fluctuations and velocity fluctuations this approach initiated in an earlier note ruelle 2012 is pursued here more carefully in particular we derive probability distributions at finite reynolds number for the dissipation and velocity fluctuations and the latter permit an interpretation of numerical experiments schumacher preprint 2014 specifically if p z dz is the probability distribution of the radial velocity gradient we can explain why when the reynolds number mathcal r increases ln p z passes from a concave to a linear then to a convex profile for large z as observed in schumacher 2014 we show that the central limit theorem applies to the dissipation and velocity distribution functions so that a logical relation with the lognormal theory of kolmogorov j fluid mech 13 82 85 1962 and obukhov is established we find however that the lognormal behavior of the distribution functions fails at large value of the argument so that a lognormal theory cannot correctly predict the exponents tau p and zeta p

unifying iteration rule for fractal objects we introduce an iteration rule for real numbers capable to generate attractors with dragon snowflake sponge or swiss flag like cross sections the idea behind it is the mapping of a torus into two or more shrunken and twisted tori located inside the previous one three distinct parameters define the symmetry the dimension and the connectedness or disconnectedness of the fractal object for some selected triples of parameter values a couple of well known fractal geometries e g the cantor set the sierpinski gasket or the swiss flag can be gained as special cases

coupled map lattices as models of deterministic and stochastic differential delay equations we discuss the probabilistic properties of a class of differential delay equations dde s by first reducing the equations to coupled map lattices and then considering the spectral properties of the associated transfer operators the analysis is carried out for the deterministic case and a stochastic case perturbed by additive or multiplicative white noise this scheme provides an explicit description of the evolution of phase space densities in dde s and yields an evolution equation that approximates the analog for delay equations of the generalized liouville and fokker planck equations it is shown that in many cases of interest for both stochastic and deterministic delay equations the phase space densities reach a limit cycle in the asymptotic regime this statistical cycling is observed numerically in continuous time systems with delay and discussed in light of our analytical description of the transfer operators 1995 the american physical society

reduced order modeling of multiscreen frequency selective surfaces using krylov based rational interpolation a method is presented for generating a broad band rational interpolant approximation of the reflection coefficient of multiple screen frequency selective surfaces fsss the technique is structured around a linearization of the system provided by a spectral domain moment method based analysis of the fss followed by a model order reduction of the linearized system using the dual rational arnoldi method this process creates a rational interpolant of the linearized system that matches its transfer function and its derivatives at several expansion points in the laplace domain numerical results indicate that a reduced order model with a system matrix of dimension less than 20 spl times 20 can accurately reproduce the broad band behavior of multiscreen fsss originally modeled with several hundreds or thousands of unknowns

dynamical systems of langevin type abstract dynamical systems of langevin type are deterministic mappings that arise if the gaussian white noise of a langevin equation is replaced by a deterministic chaotic dynamics we describe the various types of mappings that can be obtained in this way and investigate typical transition scenarios from complicated non gaussian to langevin like behavior that occur if a time scale parameter is changed we define a new characteristic quantify fir ergodic mappings called effective langevin radius which is related to the critical time scale where the marginal invariant density of the dynamical system of langevin type loses its differentiability the invariant density is shown to contain useful information on the entire characteristic functional of the chaotic driving force some general symmetry properties of the invariant densities are discussed

improved model based parameter estimation approach for accelerated periodic method of moments solutions with application to the analysis of convoluted frequency selected surfaces and metamaterials an improved smart interpolation approach known as model based parameter estimation mbpe is applied to the wide band interpolation of periodic method of moments pmm impedance matrices for normal and oblique incidence cases prior to interpolation easy to calculate but hard to interpolate phase terms are removed from the impedance matrices an efficient spectral domain pmm formulation is introduced for the accelerated analysis of frequency selective surface fss problems with a large number of unknowns employing a one dimensional o n log n fft based method to speed up the computation of matrix vector products within the bi conjugate gradient bcg iterative solver which is made possible by the asymmetric multilevel block toeplitz structure of the impedance matrix the mbpe interpolation algorithm provides a faster matrix fill time than the brute force method and is comparable or even faster than the 2 d fft based method for a large number of unknowns it also has the advantage that it can be applied to non uniform gridding cases the accuracy and efficiency of the proposed techniques for large fss problems are demonstrated by several design examples for both the normal and oblique incidence cases we also apply this efficient analysis tool to the design of multiband single layer fss filters and artificial magnetic conductors amc comprised of a 2 d periodic arrangement of convoluted metallic strips in the shape of a hilbert curve the multiband properties of the hilbert curve fss filters are studied for different iteration orders i e different degrees of space filling