theorems about the attractor for incompressible non newtonian flow driven by external forces that are rapidly oscillating in time but have a smooth average this paper discusses the incompressible non newtonian fluid with rapidly oscillating external forces g x t g x t t possessing the average g 0 x t as 0 where 0 0 then we establish that the hausdorff distance between the uniform attractors a v and a 0 v in space v is also less than o as 0 finally we show a a v for each 0 0

generalized differential encoding a nonlinear signal processing perspective incoherent detection based on differential encoding has been successfully applied to phase shift keying psk signals because it eliminates the need for carrier phase acquisition and tracking at the receiver this paper generalizes the idea of differential encoding by using a nonlinear transformation called multilag high order instantaneous moment ml him the ml him decoder is capable of removing the effects of phase ambiguity dopper frequency doppler rate and even higher order phase distortions the degrees of freedom offered by the different lags are exploited to optimize system performance in addition to the classical m ary psk the generalized differential encoding idea is also applied to nonconstant modulus constellations such as m ary qam and am pm

detailed balance has a counterpart in non equilibrium steady states when modelling driven steady states of matter it is common practice either to choose transition rates arbitrarily or to assume that the principle of detailed balance remains valid away from equilibrium neither of those practices is theoretically well founded hypothesizing ergodicity constrains the transition rates in driven steady states to respect relations analogous to but different from the equilibrium principle of detailed balance the constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables this prevents over description of the non equilibrium reservoir and implies that not all stochastic equations of motion are equally valid the resulting recipe for transition rates has many features in common with equilibrium statistical mechanics

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

variational formula for experimental determination of high order correlations of current fluctuations in driven systems for brownian motion of a single particle subject to a tilted periodic potential on a ring we propose a formula for experimentally determining the cumulant generating function of time averaged current without measurements of current fluctuations we first derive this formula phenomenologically on the basis of two key relations a fluctuation relation associated with onsager s principle of the least energy dissipation in a sufficiently local region and an additivity relation by which spatially inhomogeneous fluctuations can be properly considered we then derive the formula without any phenomenological assumptions we also demonstrate its practical advantage by numerical experiments

lower current large deviations for zero range processes on a ring we study lower large deviations for the current of totally asymmetric zero range processes on a ring with concave current density relation we use an approach by jensen and varadhan which has previously been applied to exclusion processes to realize current fluctuations by travelling wave density profiles corresponding to non entropic weak solutions of the hyperbolic scaling limit of the process we further establish a dynamic transition where large deviations of the current below a certain value are no longer typically attained by non entropic weak solutions but by condensed profiles where a non zero fraction of all the particles accumulates on a single fixed lattice site this leads to a general characterization of the rate function which is illustrated by providing detailed results for four generic examples of jump rates including constant rates decreasing rates unbounded sublinear rates and asymptotically linear rates our results on the dynamic transition are supported by numerical simulations using a cloning algorithm

global solution to the compressible isothermal multipolar fluid abstract the global existence of weak solutions of the initial boundary value problem in bounded domains to the system of partial differential equations for viscous compressible isothermal bipolar and multipolar fluids is proved some other properties as cavitation regularity up to the strong solution and uniqueness are discussed

on the strong solutions of one dimensional navier stokes poisson equations for compressible non newtonian fluids we study the strong solutions of 1d navier stokes poisson equations for compressible non newtonian fluids in bounded intervals the model is raised from the viscous isentropic gas flow under considering an external force and the non newtonian gravitational force term by using the iterative method we prove the local existence and uniqueness of strong solutions based on some compatibility condition the main condition is that the initial density vacuum is allowed

finite time generalization of the thermodynamic uncertainty relation for fluctuating currents in nonequilibrium steady states the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving we show that this relation holds not only for the long time limit of fluctuations as described by large deviation theory but also for fluctuations on arbitrary finite time scales this generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments for which infinite time scales are not accessible importantly often this finite time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long time limit we illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle

higher order differential phase shift keyed modulation advanced modulation demodulation techniques which are robust in the presence of phase and frequency uncertainties continue to be of interest to communication engineers the authors are particularly interested in techniques which accommodate slow channel phase and frequency variations with minimal performance degradation and which alleviate the need for phase and frequency tracking loops in the receiver they investigate the performance sensitivity to frequency offsets of a modulation technique known as binary double differential phase shift keying ddpsk and compare it to that of classical binary differential phase shift keying dpsk they also generalize their analytical results to include n sup th order m ary dpsk the ddpsk n 2 technique was first introduced in the russian literature circa 1972 and was studied more thoroughly in the late 1970s by pent and okunev they present an expression for the symbol error probability that is easy to derive and to evaluate numerically they also present graphical results that establish when as a function of the signal energy to noise ratio and normalized frequency offset binary ddpsk is preferable to binary dpsk with respect to performance in additive white gaussian noise finally they provide insight into the optimum receiver from a detection theory viewpoint

partial regularity of suitable weak solutions to the system of the incompressible non newtonian fluids abstract in this paper we investigate the partial regularity of the generalized solutions which are called the suitable weak solutions to the modified navier stokes equations which describes the dynamics of the incompressible monopolar non newtonian fluids it is proved that the singular points are concentrated on a closed set whose 5 2p for p 5 2 dimensional hausdorff measure is zero and the solution is a regular one for p 5 2

multiple symbol double differential detection based on least squares and generalized likelihood ratio criteria two algorithms for double differential detection of multiple phase shift keying modulation are proposed based on a least squares criterion and a generalized likelihood ratio test respectively while both algorithms take advantage of the performance gain obtained by observing the received signal over an observation interval longer than that required for symbol by symbol detection the former has the important advantage of reduced implementation complexity whereas the latter offers better performance

h2 compact attractor for a non newtonian system in two dimensional unbounded domains abstract in this paper the authors study the long time behavior of a non newtonian system in two dimensional unbounded domains they prove the existence of h2 compact attractor for the system by showing the corresponding semigroup is asymptotically compact

a new proof of the caffarelli kohn nirenberg theorem here we give a self contained new proof of the partial regularity theorems for solutions of incompressible navier stokes equations in three spatial dimensions these results were originally due to scheffer and caffarelli kohn and nirenberg our proof is much more direct and simpler 1998 john wiley sons inc

estimation and classification of polynomial phase signals the measurement of the parameters of complex signals with constant amplitude and polynomial phase measured in additive noise is considered a novel new integral transform that is adapted for signals of this type is introduced this transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance the algorithms are extended to constant amplitude and continuous nonpolynomial phase signals

existence and uniqueness of solutions for a class of non newtonian fluids with vacuum and damping abstract in this paper we proved local existence and uniqueness of solutions for a class of non newtonian fluids with vacuum and damping in one dimensional bounded intervals the main difficulty is due to the strong nonlinearity of the system and initial vacuum

large deviations of the current for driven periodic diffusions we study the large deviations of the time integrated current for a driven diffusion on the circle often used as a model of nonequilibrium systems we obtain the large deviation functions describing the current fluctuations using a fourier bloch decomposition of the so called tilted generator and we also construct from this decomposition the effective biased auxiliary or driven markov process describing the diffusion as current fluctuations are observed in time this effective process provides a clear physical explanation of the various fluctuation regimes observed it is used here to obtain an upper bound on the current large deviation function which we compare to a recently derived entropic bound and to study the low noise limit of large deviations

an improved l2 decay for weak solutions of a boussinesq system in exterior domains abstract the algebraic decay for the total kinetic energy of weak solutions of the viscous boussinesq system in an exterior domain is given by means of the spectral analysis method of the stokes operator which gives a positive answer to the l 2 decay question in 11

a note on the asymptotic smoothing effect of solutions to a non newtonian system in 2 d unbounded domains abstract in this note the authors consider the regularity of the global attractor for a non newtonian system in two dimensional unbounded domains they prove that the l 2 compact attractor and the h 2 compact attractor of the system are the same and thus establish the asymptotic smoothing effect of solutions to this system

time decay rates of non newtonian flows in rn abstract this paper is concerned with time decay rates of the weak solutions of an incompressible non newtonian fluid motion model in half spaces r n for n 3 with the use of the spectral decomposition of the stokes operator and l p l q estimates it is shown that the weak solutions decay in l 2 norm like t n 2 1 r 1 2 when the initial velocity u 0 l 2 l r for 1 r 2 the higher decay rates t n 2 1 r 1 2 1 2 are obtained if u 0 satisfies the additional moment condition r n x n u 0 x r d x 1 r 2 moreover the error estimates between the non newtonian flow and the navier stokes flow are discussed

existence and uniqueness of solutions for a class of non newtonian fluids with singularity and vacuum abstract the aims of this paper are to discuss existence and uniqueness of local solutions for a class of non newtonian fluids with singularity and vacuum in one dimensional bounded intervals there are two important points in this paper one is that we allow the initial vacuum another one is that the viscosity term of momentum equation is with singularity and fully nonlinearity

pullback attractors for a non autonomous incompressible non newtonian fluid this paper studies the pullback asymptotic behavior of solutions for a non autonomous incompressible non newtonian fluid in two dimensional 2d bounded domains we first prove the existence of pullback attractors av in space v has h2 regularity see notation in section 2 and ah in space h has l2 regularity for the cocycle corresponding to the solutions of the fluid then we verify the regularity of the pullback attractors by showing av ah which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data

non equivalence of dynamical ensembles and emergent non ergodicity dynamical ensembles have been introduced to study constrained stochastic processes in the microcanonical ensemble the value of a dynamical observable is constrained to a given value in the canonical ensemble a bias is introduced in the process to move the mean value of this observable the equivalence between the two ensembles means that calculations in one or the other ensemble lead to the same result in this paper we study the physical conditions associated with ensemble equivalence and the consequences of non equivalence for continuous time markov jump processes we show that ergodicity guarantees ensemble equivalence for non ergodic systems or systems with emergent ergodicity breaking we adapt a method developed for equilibrium ensembles to compute asymptotic probabilities while caring about the initial condition we illustrate our results on the infinite range ising model by characterizing the fluctuations of magnetization and activity we discuss the emergence of non ergodicity by showing that the initial condition can only be forgotten after a time that scales exponentially with the number of spins

existence regularity and decay rate of solutions of non newtonian flow the existence and the regularity of young measure valued solutions to non newtonian flows are considered furthermore the uniqueness of solutions and their asymptotic behavior are given

asymptotic stability of non newtonian flows with large perturbation in r2 consider asymptotic stability of weak solutions for the incompressible non newtonian fluid motion in whole spaces r 2 we shall show that although the initial data disturbance from u are large every perturbed flow v with the energy inequality converges asymptotically to u as v t u t 0 as t

tightening the uncertainty principle for stochastic currents we connect two recent advances in the stochastic analysis of nonequilibrium systems the loose uncertainty principle for the currents which states that statistical errors are bounded by thermodynamic dissipation and the analysis of thermodynamic consistency of the currents in the light of symmetries employing the large deviation techniques presented by gingrich et al phys rev lett 116 120601 2016 prltao0031 900710 1103 physrevlett 116 120601 and pietzonka barato and seifert phys rev e 93 052145 2016 2470 004510 1103 physreve 93 052145 we provide a short proof of the loose uncertainty principle and prove a tighter uncertainty relation for a class of thermodynamically consistent currents j our bound involves a measure of partial entropy production that we interpret as the least amount of entropy that a system sustaining current j can possibly produce at a given steady state we provide a complete mathematical discussion of quadratic bounds which allows one to determine which are optimal and finally we argue that the relationship for the fano factor of the entropy production rate var mean 2 is the most significant realization of the loose bound we base our analysis both on the formalism of diffusions and of markov jump processes in the light of schnakenberg s cycle analysis

uniform attractor for a two dimensional nonautonomous incompressible non newtonian fluid abstract we discuss the long time behavior of solutions for a two dimensional 2d nonautonomous incompressible non newtonian fluid in 2d bounded domains when the external force g 0 x t is translation compact tr c in l loc 2 r h we obtain the existence and reveal the structure of the uniform attractor for the processes associated to the fluid by constructing skew product flow on the extended phase space when g 0 l b 2 is properly small we establish that there exists a unique bounded asymptotically stable solution to the fluid

random attractor for the ladyzhenskaya model with additive noise this paper studies the dynamical behavior of the ladyzhenskaya model with additive noise with some conditions we prove that the generated random dynamical system has a compact random attractor which is a random compact set absorbing any bounded nonrandom subset of the phase space

universal bounds on current fluctuations for current fluctuations in nonequilibrium steady states of markovian processes we derive four different universal bounds valid beyond the gaussian regime different variants of these bounds apply to either the entropy change or any individual current e g the rate of substrate consumption in a chemical reaction or the electron current in an electronic device the bounds vary with respect to their degree of universality and tightness a universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production a second stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states these two bounds are conjectures based on extensive numerics an exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved this bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium an asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived this bound allows for the prediction of the asymptotic growth of the generating function even though our results are restricted to networks with a finite number of states we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle our bounds provide a general class of constraints for nonequilibrium systems

regularity of trajectory attractor and upper semicontinuity of global attractor for a 2d non newtonian fluid abstract there are two results within this paper the one is the regularity of trajectory attractor and the trajectory asymptotic smoothing effect of the incompressible non newtonian fluid on 2d bounded domains for which the solution to each initial value could be non unique the other is the upper semicontinuity of global attractors of the addressed fluid when the spatial domains vary from m to r l l where m m 1 is an expanding sequence of simply connected bounded and smooth subdomains of such that m as m that is let a and a m be the global attractors of the fluid corresponding to and m respectively we establish that for any neighborhood o a of a the global attractor a m enters o a if m is large enough

l2 compact uniform attractors for a nonautonomous incompressible non newtonian fluid with locally uniformly integrable external forces in distribution space we consider the long time behavior of solutions for a two dimensional nonautonomous incompressible non newtonian fluid with external forces in distribution space when the external force g0 x t is locally uniformly integrable see definition 3 1 in lloc2 r w we prove the existence of l2 compact uniform attractor in space h and reveal its structure for the families of processes corresponding to the fluid moreover if g0 lb2 r w is properly small we establish the unique existence of bounded asymptotically stable solutions and give two interesting corollaries

large deviations of the dynamical activity in the east model analysing structure in biased trajectories we consider large deviations of the dynamical activity in the east model we bias this system to larger than average activity and investigate the structure that emerges to best characterize this structure we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system we combine numerical results with linear response theory and variational estimates of these effective interactions giving the first insights into such interactions in a many body system across a wide range of biases the system exhibits a hierarchy of responses to the bias remaining quasi equilibrated on short length scales but deviating far from equilibrium on large length scales we discuss the connection between this hierarchy and the hierarchical ageing behaviour of the system

analysis of a ladyzhenskaya model for incompressible viscous flow abstract in this paper we analyze a model for the motion of incompressible viscous flows proposed by ladyzhenskaya we establish a new a priori estimate for the nonstationary model and then obtain more general existence and uniqueness results we also present some uniqueness results for the stationary model the relationship between fluid motion governed by the ladyzhenskaya model and that governed by the navier stokes equations is addressed

a large deviation perspective on ratio observables in reset processes robustness of rate functions we study large deviations of a ratio observable in discrete time reset processes the ratio takes the form of a current divided by the number of reset steps and as such it is not extensive in time a large deviation rate function can be derived for this observable via contraction from the joint probability density function of current and number of reset steps the ratio rate function is differentiable and we argue that its qualitative shape is robust i e it is generic for reset processes regardless of whether they have short or long range correlations we discuss similarities and differences with the rate function of the efficiency in stochastic thermodynamics

the heuristic glrt and map detectors for double differential modulation are identical we consider the relationship between several single symbol detectors for double differential modulation we have shown in a previous paper that a simple heuristic detector is identical to the generalized likelihood ratio test glrt detector in this correspondence we introduce a maximum a posteriori probability map detector and show that it is identical to the heuristic and glrt detectors consequently neither glrt nor map can offer any gain over the simple heuristic detector which means that the latter should be the detector of choice

analytical solutions to a class of non newtonian fluids with free boundaries we study analytical solutions to a class of non newtonian fluids with free boundaries for suitable non newtonian fluids we construct a class of analytical solutions in r with both continuous density condition and the stress free condition across the free boundaries separating the fluid from vacuum such solutions exhibit interesting new information such as the formation of vacuum as time tends to infinitely and explicit regularities and large time decay estimates of the velocity field

large time behavior to the system of incompressible non newtonian fluids in r2 abstract in this paper the authors study the large time behavior for the weak solutions to a class system of the incompressible non newtonian fluids in r 2 it is proved that the weak solutions decay in l 2 norm at 1 t 1 2 and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation

diffusions conditioned on occupation measures a markov process fluctuating away from its typical behavior can be represented in the long time limit by another markov process called the effective or driven process having the same stationary states as the original process conditioned on the fluctuation observed we construct here this driven process for diffusions spending an atypical fraction of their evolution in some region of state space corresponding mathematically to stochastic differential equations conditioned on occupation measures as an illustration we consider the langevin equation conditioned on staying for a fraction of time in different intervals of the real line including the positive half line which leads to a generalization of the brownian meander problem other applications related to quasi stationary distributions metastable states noisy chemical reactions queues and random walks are discussed

a fast and accurate single frequency estimator a novel frequency estimator for a single complex sinusoid in complex white gaussian noise is proposed the estimator is more computationally efficient that the optimal maximum likelihood estimator yet attains equally good performance at moderately high signal to noise ratios the estimator is shown to be related to the linear prediction estimator this relationship is used to reveal why the linear prediction estimator does not attain the cramer rao bound even at high signal to noise ratios

large deviation function for entropy production in driven one dimensional systems the large deviation function for entropy production is calculated by solving a time independent eigenvalue problem for a particle driven along a periodic potential in an intermediate force regime the large deviation function shows pronounced deviations from a gaussian behavior with a characteristic kink at zero entropy production such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range

transition probabilities and dynamic structure function in the asep conditioned on strong flux we consider the asymmetric simple exclusion processes asep on a ring constrained to produce an atypically large flux or an extreme activity using quantum free fermion techniques we find the time dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics in the thermodynamic limit we obtain the explicit scaling form this gives a direct proof that the dynamical exponent in the extreme current regime is z 1 rather than the kpz exponent z 3 2 which characterizes the asep in the regime of typical currents some of our results extend to the activity in the partially asymmetric simple exclusion process including the symmetric case

uniform attractors for nonautonomous incompressible non newtonian fluid with locally uniform integrable external forces this paper discusses the long time behavior of solutions for a two dimensional 2d nonautonomous incompressible non newtonian fluid in 2d bounded domains when the external force g0 x t is locally uniform integrable see definition 1 1 in lloc2 r h the authors obtain the existence and structure of uniform attractors in space v for the family of processes associated with the fluid moreover when g0 lb2 is properly small they provide some interesting corollaries

characterizing filtered light waves corrupted by phase noise the phase noise associated with single mode semiconductor lasers must be accounted for in performance studies of lightwave communication systems the standard phase noise model is a brownian motion stochastic process although many analyses of lightwave communication systems have been published none to the authors knowledge has fully adhered to the standard model the reason is that a proper characterization of filtered lightwave signal had not been achieved such a characterization along with theoretical approaches to obtaining it is detailed the authors show for example how to generate probability density functions pdfs of the magnitude of a filtered laser tone with special attention to the tail region and how to analytically represent the characteristic function of the pdf in closed form in the small phase noise realm with the characterization in place the stage is now set for determining the bit error rate performance of advanced detection techniques which seek to mitigate the phase noise impairment

global strong solutions of a class of non newtonian fluids with small initial energy abstract in this paper we are concerned with an initial boundary value problem for a class of non newtonian fluids the viscosity term of momentum equation possesses singularity and nonlinearity and the initial vacuum is allowed the main feature which distinguishes this paper from other related works lies in the fact that we study the global strong solution of the compressible non newtonian fluids with singularity and vacuum in one dimensional bounded intervals and show that there exists a unique global in time strong solution to the problem while the initial energy is small

large deviations of random walks on random graphs we study the rare fluctuations or large deviations of time integrated functionals or observables of an unbiased random walk evolving on erdos renyi random graphs and construct a modified biased random walk that explains how these fluctuations arise in the long time limit two observables are considered the sum of the degrees visited by the random walk and the sum of their logarithm related to the trajectory entropy the modified random walk is used for both quantities to explain how sudden changes in degree fluctuations similar to dynamical phase transitions are related to localization transitions for the second quantity we also establish links between the large deviations of the trajectory entropy and the maximum entropy random walk

maximum likelihood double differential detection clarified the maximum likelihood detector mld also called the generalized likelihood ratio test glrt detector for single differential modulation is easy to derive on the other hand the mld problem associated with double differential modulation is much more complicated and solving it was deemed to require a computationally unattractive nonlinear search consequently a simple heuristic detector was usually preferred to the mld on computational grounds in this correspondence we prove the somewhat unexpected result that the aforementioned heuristic detector coincides with the exact mld

on partial regularity results for the navier stokes equations looking at the regularity results of scheffer respectively caffarelli kohn and nirenberg from a new point of view indicates that estimates for the pressure do not play an essential role in partial regularity results for the navier stokes equations

global classical solution to a one dimensional compressible non newtonian fluid with large initial data and vacuum abstract because of the stronger nonlinearity and degeneracies of the density due to the momentum equation and appearance of vacuum there are few results until now about global existence of classical solution to a compressible non newtonian fluid in this paper the global in time existence and uniqueness of classical solution to the initial boundary value problem is established for a one dimensional compressible non newtonian fluid with large initial data and vacuum our analysis is based on some delicate energy estimates together with the iterate method being used ingeniously

trajectory attractor and global attractor for a two dimensional incompressible non newtonian fluid the authors construct the trajectory attractor and global attractor for an autonomous two dimensional non newtonian fluid

efficiency fluctuations in steady state machines we study the statistics of the efficiency in a class of isothermal cyclic machines with realistic coupling between the internal degrees of freedom we derive under fairly general assumptions the probability distribution function for the efficiency we find that the macroscopic efficiency is always equal to the most likely efficiency and it lies in an interval whose boundaries are universal as they only depend on the input and output thermodynamic forces and not on the details of the machine the machine achieves the upper boundary of such an interval only in the limit of tight coupling furthermore we find that the tight coupling limit is a necessary yet not sufficient condition for the engine to perform close to the reversible efficiency the reversible efficiency is the least likely regardless of the coupling strength in agreement with previous studies by using a large deviation formalism we derive a fluctuation relation for the efficiency which holds for any number of internal degrees of freedom in the system

thermodynamic formula for the cumulant generating function of time averaged current the cumulant generating function of time averaged current is studied from an operational viewpoint specifically for interacting brownian particles under nonequilibrium conditions we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added where the modified system is characterized by a variational principle the formula reminds us of einstein s fluctuation theory in equilibrium statistical mechanics furthermore since the formula leads to the fluctuation dissipation relation when the linear response regime is focused on it is regarded as an extension of the linear response theory to that valid beyond the linear response regime the formula is also related to previously known theories such as the donsker varadhan theory the additivity principle and the least dissipation principle but it is not derived from them examples of its application are presented for a driven brownian particle on a ring subject to a periodic potential

large deviations conditioned on large deviations i markov chain and langevin equation we present a systematic analysis of stochastic processes conditioned on an empirical observable q t defined in a time interval 0 t for large t we build our analysis starting with a discrete time markov chain results for a continuous time markov process and langevin dynamics are derived as limiting cases in the large t limit we show how conditioning on a value of q t modifies the dynamics for a langevin dynamics with weak noise and conditioned on q t we introduce large deviation functions and calculate them using either a wkb method or a variational formulation this allows us in particular to calculate the typical trajectory and the fluctuations around this trajectory when conditioned on a certain value of q t for large t

double differential space time block coding for time selective fading channels most existing space time coding schemes assume time invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver other single differential space time block coding schemes forego channel estimation but are less effective in rapidly fading environments based on a diagonal unitary matrix group a novel double differential space time block coding approach is derived in this paper for time selective fading channels without estimating the channels at the receiver information symbols are recovered with antenna diversity gains regardless of frequency offsets the resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas approximately optimal space time codes are also designed to minimize bit error rate system performance is evaluated both analytically and with simulations

the convergence of non newtonian fluids to navier stokes equations abstract in this paper the convergence of solutions for incompressible dipolar viscous non newtonian fluids is investigated we obtain the conclusion that the solutions of non newtonian fluids converge to the solutions of navier stokes equations in the sense of l 2 norm resp h 1 norm as the viscosities tend to zero and the initial data belong to h 1 resp h 2 moreover we obtain l norm convergence of solutions if the initial data belong to h 2

regularity criterion for generalized newtonian fluids in bounded domains abstract the regularity of a non newtonian flow in a domain with a boundary cannot be treated easily because of the nonlinear viscosity term and the global property of the pressure a distance function was used in a previous study to obtain a strong solution in the present study using the distance function idea we obtain serrin type regularity criteria for the vorticity and the velocity with regard to non newtonian equations with shear dependent viscosity in a bounded domain

pullback asymptotic behavior of solutions for a non autonomous non newtonian fluid on two dimensional unbounded domains this paper studies the pullback asymptotic behavior of solutions for a non autonomous non newtonian fluid on r l l for some l 0 we first use the technique of truncation functions together with the decomposition of spatial domain to prove the existence of a pullback attractor in then we discuss the upper semicontinuity of the pullback attractors when the spatial domains vary from m to where m m 1 is an expanding sequence of simply connected bounded and smooth subdomains of such that m 1 m let a a r and am am r be the pullback attractors corresponding to and m respectively we establish for each r that for any neighborhood o a of a am enters o a if m is large enough

convergence analysis for incompressible generalized newtonian fluid flows with nonstandard anisotropic growth conditions we study equations to describe incompressible generalized newtonian fluids where the extra stress tensor satisfies a nonstandard anisotropic asymptotic growth condition an implicit finite element discretization and a simple fully practical fixed point scheme with proper thresholding criterion are proposed and convergence toward weak solutions of the limiting problem is shown computational experiments are included which motivate nontrivial fluid flow behavior

the global attractor for the 2d navier stokes flow on some unbounded domains we extend previous results on the existence of the global attractor for the 2d navier stokes equations on some unbounded domains in the sense that the forcing term need not lie in any weighted space nor is the boundary of the domain required to be smooth the existence of the global attractor is obtained on arbitrary open sets such that the poincare inequality holds and for forces in the natural dual space v the proof is based on the energy equation and the concept of asymptotic compactness an estimate of the hausdorff and fractal dimensions of the attractor is also given

a finite dimensional attractor for three dimensional flow of incompressible fluids abstract the asymptotic behavior of the flow for a system of the navier stokes type is investigated in the considered model the viscous part of the stress tensor is generally a nonlinear function of the symmetric part of the velocity gradient provided that the function describing this dependence satisfies the polynomial p 1 growth condition a unique weak solution exists if either p 2 n 2 and u 0 h or p 1 2 n n 2 and u 0 w 1 2 c n h in the first case the existence of a global attractor in h is proved in order to indicate the finite dimensional behavior of the flow at infinity the fractal dimension of the new invariant set composed from all short trajectories with initial value in the attractor is estimated in the l 2 0 h topology having uniqueness only for more regular data in the second case many trajectories can start from the initial value u 0 h this does not allow one to define a semigroup on the space h therefore the set of short trajectories x s closed in l 2 0 h is introduced along with a semigroup working on this set the existence of a global attractor with a finite fractal dimension is then demonstrated

existence and finite dimensionality of the global attractor for evolution equations on unbounded domains abstract this paper is devoted to the asymptotic behavior for some evolution equations when the underlying euclidean domain is unbounded we present a method that is able to overcome the lack of compactness of the trajectories in such situations and that allows us to obtain some results on the global attractor similar to those on bounded domains this method is based on the utilization of an appropriate weight integration function that depends on x and t and becomes effective in x for large t s

direct evaluation of dynamical large deviation rate functions using a variational ansatz we describe a simple form of importance sampling designed to bound and compute large deviation rate functions for time extensive dynamical observables in continuous time markov chains we start with a model defined by a set of rates and a time extensive dynamical observable we construct a reference model a variational ansatz for the behavior of the original model conditioned on atypical values of the observable direct simulation of the reference model provides an upper bound on the large deviation rate function associated with the original model an estimate of the tightness of the bound and if the ansatz is chosen well the exact rate function the exact rare behavior of the original model does not need to be known in advance we use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature straightforward ansatze yield bounds that are tighter than bounds obtained from level 2 5 of large deviations via approximations that involve uniform scalings of rates we show how to correct these bounds in order to recover the rate functions exactly our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution

non equilibrium current fluctuations in stochastic lattice gases we study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles more precisely we establish a large deviation principle for a space time fluctuation j of the empirical current with a rate functional i j we then estimate the probability of a fluctuation of the average current over a large time interval this probability can be obtained by solving a variational problem for the functional i we discuss several possible scenarios interpreted as dynamical phase transitions for this variational problem they actually occur in specific models we finally discuss the time reversal properties of i and derive a fluctuation relationship akin to the gallavotti cohen theorem for the entropy production