identification of shear buildings using an instrumental variable method and linear integral filters abstract this paper develops a method for estimating the parameters of a seismically excited building acceleration measurements of the ground and of the building floors containing offsets and noise are used for identification purposes the proposed scheme estimates the complete model of the building if all the floors are equipped with accelerometers moreover it also estimates a reduced model of the structure if only some floors are instrumented the methodology is based on the combined use of the instrumental variable method and linear integral filters the instrumental variable method employs as instrument an auxiliary model of the structure and it is able to directly identify the continuous time structure model using discrete time data without resorting on model transformations from continuous time to discrete time and vice versa using linear integral filters allows obtaining a linear in the parameters expression that depends only on acceleration measurements suitable for parameter identification purposes these filters eliminate measurement offsets and attenuate high frequency measurement noise the above features together with the use of the instrumental variable method reduce the likelihood of biased parameter estimates experiments on a testbed employing a reduced scale five story structure allow comparing the results obtained using the instrumental variable method and those produced by the standard least squares method

nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

multiplicity of time periodic solutions and their stabilities for quasigeostrophic equations in this article we study the quasigeostrophic equation which is a prototypical geophysical fluid model we will show the existence of multiple time periodic solutions and study their stabilities we also prove the exponential decaying of solutions to the initial value problem with small initial data

bifurcating periodic solutions of wind driven circulation equations the existence of bifurcating periodic flows in a quasi geostrophic mathematical model of wind driven circulation is investigated in the model the ekman number r and reynolds number r control the stability of the motion of the fluid through rigorous analysis it is proved that when the basic steady state solution is independent of the ekman number then a spectral simplicity condition is sufficient to ensure the existence of periodic solutions branching off the basic steady state solution as the ekman number varies across its critical value for constant reynolds number when the basic solution is a function of ekman number an additional condition is required to ensure periodic solutions

quantum fluctuation relations for the lindblad master equation an open quantum system interacting with its environment can be modeled under suitable assumptions as a markov process described by a lindblad master equation in this work we derive a general set of fluctuation relations for systems governed by a lindblad equation these identities provide quantum versions of jarzynski hatano sasa and crooks relations in the linear response regime these fluctuation relations yield a fluctuation dissipation theorem fdt valid for a stationary state arbitrarily far from equilibrium for a closed system this fdt reduces to the celebrated callen welton kubo formula

localisation in a cosserat continuum under static and dynamic loading conditions abstract localisation studies have been carried out for an unconstrained elasto plastic strain softening cosserat continuum because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement a finite constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions because of the existence of rotational degrees of freedom in a cosserat continuum additional wave types arise and wave propagation becomes dispersive this has been investigated analytically and numerically for an elastic cosserat continuum and an excellent agreement has been found between both solutions

attractors for the 3d baroclinic quasi geostrophic equations of large scale atmosphere abstract the existence of absorbing sets and a compact connected global attractor to the 3d baroclinic quasi geostrophic equations of large scale atmosphere are obtained using cft theory an upper bound of the hausdorff and fractal dimensions of the global attractor in terms of the physically relevant parameters re the reynolds number ro the rossby number and f is derived moreover similar results are also established for the 2d vorticity equations of globe atmosphere

asymptotic convergence rate of supercritical surface quasi geostrophic equation in morrey space abstract in this paper the asymptotic convergence rate of the supercritical surface quasi geostrophic equation in morrey space is investigated it is shown that if the global solution x t of the supercritical surface quasi geostrophic equation satisfies the growth condition in critical morrey space 0 t m p q r 2 r d t for r 2 p 2 p then every perturbed weak solution x t of the perturbed quasi geostrophic equation converges asymptotically to x t with the optimal rate t t l 2 o 1 t 1 as t in particular the initial perturbation is allowed large the findings are based on the spectral decomposition methods of fractional laplace and morrey space technique

fluctuation theorems for quantum master equations a quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i e a quantum master equation qme quantum trajectories and their associated entropy heat and work appear naturally by transforming the qme to a time dependent liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem a quantum integral fluctuation theorem a steady state fluctuation theorem and the jarzynski relation are derived in a similar way as for classical stochastic dynamics

nonextensive triangle equality and other properties of tsallis relative entropy minimization kullback leibler relative entropy has unique properties in cases involving distributions resulting from relative entropy minimization tsallis relative entropy is a one parameter generalization of kullback leibier relative entropy in the nonextensive thermostatistics in this paper we present the properties of tsallis relative entropy minimization and present some differences with the classical case in the representation of such a minimum relative entropy distribution we highlight the use of the q product an operator that has been recently introduced to derive the mathematical structure behind the tsallis statistics one of our main results is the generalization of triangle equality of relative entropy minimization to the nonextensive case

quantum work fluctuations versus macrorealism in terms of non extensive entropies abstract fluctuations of the work performed on a driven quantum system can be characterized by the so called fluctuation theorems the jarzynski relation and the crooks theorem are famous examples of exact equalities characterizing non equilibrium dynamics such statistical theorems are typically formulated in a similar manner in both classical and quantum physics leggett garg inequalities are inspired by the two assumptions referred to as the macroscopic realism and the non invasive measurability together these assumptions are known as the macrorealism in the broad sense quantum mechanics is provably incompatible with restrictions of the leggett garg type it turned out that leggett garg inequalities can be used to distinguish quantum and classical work fluctuations we develop this issue with the use of entropic functions of the tsallis type varying the entropic parameter we are often able to reach more robust detection of violations of the corresponding leggett garg inequalities in reality all measurement devices suffer from losses within the entropic formulation detection inefficiencies can naturally be incorporated into the consideration this question also shows advantages that are provided due to the use of generalized entropies

taylor impact test revisited determination of plasticity parameters for metals at high strain rate abstract taylor impact test is the simplest experimental approach for characterizing plastic behaviour of metals under high strain rate up to 105 s 1 herein a cylindrical rod is impacted upon a rigid stationary anvil and the dynamic yield strength is estimated by comparing the experimentally obtained rod deformation with its theoretical counterpart despite being simple and potent concept the lack of a comprehensive theoretical model which relates the material constitutive with the deformation pattern of the rod has so far restricted the use of the taylor impact test in material characterization in the present study the taylor impact test is revisited and an attempt is made to formulate an inverse framework for efficient determination of constitutive parameters for metals the inverse analysis is performed via the extended kalman filter technique where the forward model is constituted based on the derivation given in chakraborty et al 2015 unlike the common practice for better estimation of material constants the deformation time histories are also included in the present inverse formulation for demonstration five different plasticity models viz johnson cook model zerilli armstrong model steinberg cochran guinan lund model mechanical threshold stress model and preston tonks wallace model are considered the estimated parameters are found to be in good agreement with their reference values it is shown that the most distinguished feature of the present attempt is that a single taylor test is sufficient to determine the parameters with reasonable accuracy

fluctuation theorems work is not an observable the characteristic function of the work performed by an external time dependent force on a hamiltonian quantum system is identified with the time ordered correlation function of the exponentiated system s hamiltonian a similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the jarzynski work theorem

the index of a quantum dynamical semigroup a numerical index is introduced for semigroups of completely positive maps of b h which generalizes the index ofe0 semigroups it is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to ane0 semigroup provided that the dilation isminimal

space and time localization for the estimation of distributed parameters in a finite element model abstract in this paper we study the problem of estimating the possibly non homogeneous material coefficients inside a physical system from transient excitations and measurements made in a few points on the boundary we assume there is available an adequate finite element fem model of the system whose distributed physical parameters must be estimated from the experimental data we propose a space time localization approach that gives a better conditioned estimation problem without the need of an expensive regularization some experimental results obtained on an elastic system with random coefficients are given

real time updating of structural mechanics models using kalman filtering modified constitutive relation error and proper generalized decomposition the paper aims at proposing a new strategy for real time identification or updating of structural mechanics models defined as dynamical systems the main idea is to introduce the modified constitutive relation error concept which is a practical tool that enables to efficiently solve identification problems with highly corrupted data into the kalman filtering which is a classical framework for data assimilation furthermore a pgd based model reduction method is performed in order to optimize capabilities of the online updating strategy performances of the proposed approach in terms of robustness gain and computational cost reduction are illustrated on several unsteady thermal applications

equilibrium states of the charney devore quasi geostrophic equation in mid latitude atmosphere on the predictability of atmospheric blocking in the mid latitude atmosphere a quasi geostrophic beta plane channel model equation was introduced in a pioneering work by charney and devore in 1979 based on the understanding of quasi stationary weather patterns the equation is driven by a zonal thermal flow representing a mid latitude westerly jet and a wave function representing an ocean land topography they truncated the equation into a three spectral mode model which gives rise to the existence of multiple equilibrium states showing a blocking mechanism profile moreover they predicted numerically the absence of the multiple equilibrium states with respect to the flat topography situation in the present paper this absence observation is discussed from rigorous analysis and the coexistence of two stable equilibrium states similarly to the three mode model equilibrium states accounting for atmospheric blocking is investigated numerically with the increment of topographic amplitude

nonequilibrium potential and fluctuation theorems for quantum maps we derive a general fluctuation theorem for quantum maps the theorem applies to a broad class of quantum dynamics such as unitary evolution decoherence thermalization and other types of evolution for quantum open systems the theorem reproduces well known fluctuation theorems in a single and simplified framework and extends the hatano sasa theorem to quantum nonequilibrium processes moreover it helps to elucidate the physical nature of the environment that induces a given dynamics in an open quantum system

new forms of extended kalman filter via transversal linearization and applications to structural system identification two novel forms of the extended kalman filter ekf are proposed for parameter estimation in the context of problems of interest in structural mechanics these filters are based on variants of the derivative free locally transversal linearization ltl and multi step transversal linearization mtrl schemes thus unlike the conventional ekf the proposed filters do not need computing jacobian matrices at any stage while the ltl based filter provides a single step procedure the mtrl based filter works over multiple time steps and finds the system transition matrix of the conditionally linearized vector field through magnus expansion other major advantages of the new filters over the conventional ekf are in their superior numerical accuracy and considerably less sensitivity to the choice of timestep sizes a host of numerical illustrations covering single as well as multi degree of freedom oscillators with time invariant parameters and those with discontinuous temporal variations are presented to confirm the numerical advantages of the novel forms of ekf over the conventional one

stability and bifurcation of the taylor problem the main objective of this paper is to address the stability and bifurcation of the couette flow between two concentric rotating cylinders and to verify rigorously taylor s observation in his experiments 13 a nonlinear theory is obtained for the taylor problem leading in particular to rigorous justifications of the linear theory used by physicists and the taylor vortex structure the main technical tools are the dynamic bifurcation theory and the geometric theory for incompressible flows both developed recently by ma wang 10 12

properties of q entropies basic properties of the q entropy sq q 1 1 1 tr q 0 q 1 for states of a quantum system are established concavity quasi convexity continuity and failure of additivity and subadditivity for composite systems

information theoretic bell inequalities we formulate information theoretic bell inequalities which apply to any pair of widely separated physical systems if local realism holds the two systems must carry information consistent with the inequalities two spin s particles in a state of zero total spin violate these information bell inequalities

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

hopf bifurcation in quasi geostrophic channel flow in this article we conduct a rigorous stability and bifurcation analysis for a highly idealized model of planetary scale atmospheric and oceanic flows the model is governed by the two dimensional quasi geostrophic equation for the conservation of vorticity in an east west oriented periodic channel the main result is the existence of hopf bifurcation of the flow as the reynolds number crosses a critical value the key idea in proving this result is translating the eigenvalue problem into a difference equation and treating the latter by continued fraction methods numerical results are obtained by using a finite difference scheme with high spatial resolution and these results agree closely with the theoretical predictions the spatio temporal structure of the limit cycle corresponds to a wave that propagates slowly westward and is symmetric about the midaxis of the channel for plausible paramater values that correspond to midlatitude atmospheric flows the period of this wave is 20 25 days

detailed balance as a quantum group symmetry of kraus operators a unital completely positive map governing the time evolution of a quantum system is usually called a quantum channel and it can be represented by a tuple of operators which are then referred to as the kraus operators of the channel we look at states of the system whose correlations with respect to the channel have a certain symmetry then we show that detailed balance holds if the kraus operators satisfy a very interesting algebraic relation which plays an important role in the representation theory of any compact quantum group

formation of singularities for a transport equation with nonlocal velocity we study a 1d transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data by adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time

entropy production for quantum markov semigroups an invariant state of a quantum markov semigroup is an equilibrium state if it satisfies a quantum detailed balance condition in this paper we introduce a notion of entropy production for faithful normal invariant states of a quantum markov semigroup on mathcal b mathsf h as a numerical index measuring how far they are from equilibrium the entropy production rate is defined as the derivative of the relative entropy of the one step forward and backward evolution in analogy with the classical probabilistic concept we prove an explicit trace formula expressing the entropy production rate in terms of the completely positive part of the generator of a norm continuous quantum markov semigroup showing that it turns out to be zero if and only if a standard quantum detailed balance condition holds

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

vanishing viscosity limit for global attractors for the damped navier stokes system with stress free boundary conditions abstract we consider the damped and driven navier stokes system with stress free boundary conditions and the damped euler system in a bounded domain r 2 we show that the damped euler system has a strong global attractor in h 1 we also show that in the vanishing viscosity limit the global attractors of the navier stokes system converge in the non symmetric hausdorff distance in h 1 to the strong global attractor of the limiting damped euler system whose solutions are not necessarily unique

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

operator algebras and subproduct systems arising from stochastic matrices we study subproduct systems in the sense of shalit and solel arising from stochastic matrices on countable state spaces and their associated operator algebras we focus on the non self adjoint tensor algebra and viselter s generalization of the cuntz pimsner c algebra to the context of subproduct systems suppose that x and y are arveson stinespring subproduct systems associated to two stochastic matrices over a countable set and let t x and t y be their tensor algebras we show that every algebraic isomorphism from t x onto t y is automatically bounded furthermore t x and t y are isometrically isomorphic if and only if x and y are unitarily isomorphic up to a automorphism of l when is finite we prove that t x and t y are algebraically isomorphic if and only if there exists a similarity between x and y up to a automorphism of l moreover we provide an explicit description of the cuntz pimsner algebra o x in the case where is finite and the stochastic matrix is essential

calculating work in adiabatic two level quantum markovian master equations a characteristic function method we present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two level quantum markovian master equations these systems are steered by some slowly varying parameters and the dissipations may depend on time our theory is based on the interpretation of the quantum jump for the master equations in addition to the calculation we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions which is exactly the same as in the case of isolated systems a periodically driven two level model is used to demonstrate the method

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

steady state bifurcation analysis of a strong nonlinear atmospheric vorticity equation the quasi geostrophic vorticity equation studied in the present paper is a simplified form of the atmospheric circulation model introduced by charney and devore j atmos sci 36 1979 1205 1216 on the existence of multiple steady states to the understanding of the persistence of atmospheric blocking the fluid motion defined by the equation is driven by a zonal thermal forcing and an ekman friction forcing measured by it is proved that the steady state solution is globally unique for large values while multiple steady state solutions branch off the basic steady state solution for crit where the critical value crit is less than one without involvement of viscosity the equation has fully non linear property as its non linear part contains the highest order derivative term steady state bifurcation analysis is essentially based on the compactness which can be simply obtained for semilinear equations such as the navier stokes equations but is not available for the fully nonlinear quasi geostrophic vorticity equation in the euler formulation therefore the lagrangian formulation of the equation is employed to gain the required compactness

computational design for long term numerical integration of the equations of fluid motion the integral constraints on quadratic quantities of physical importance such as conservation of mean kinetic energy and mean square vorticity will not be maintained in finite difference analogues of the equation of motion for two dimensional incompressible flow unless the finite difference jacobian expression for the advection term is restricted to a form which properly represents the interaction between grid points as derived in this paper it is shown that the derived form of the finite difference jacobian prevents nonlinear computational instability and thereby permits long term numerical integrations

parameter identification of a cohesive crack model by kalman filter abstract the kalman filter kf methodology is apt to solve parameter identification inverse problems in a statistical context through a sequence of estimations which starts from an a priori estimation by an expert bayesian approach and exploits a time stepping flow of experimental data until convergence is empirically ascertained such methodology is here adopted for the identification of the material parameters together with their uncertainties in a mode i cohesive crack model on the basis of experimental data generated by wedge splitting tests on concrete specimens the simulation of the experiments is based on the assumptions of a piecewise linear cohesive model with four parameters to identify on the crack path and of linear elasticity elsewhere in view of regularly progressive fracture processes the discrete crack model and consequently the overall finite element analysis are formulated as linear complementarity problems this mathematical construct is exploited to obtain the sensitivity matrix key ingredient of the kf extended to nonlinear inverse problems in a computationally convenient closed form various issues peculiar of kf identification in the present mechanical context are critically discussed in the light of the numerical solutions achieved

hopf bifurcation and transition of three dimensional wind driven ocean circulation problem abstract the purpose of this article is three fold the first is to investigate the linear stability of the basic flow governed by the three dimensional 3d quasi geostrophic qg equation with a steady wind force we show that the basic flow will become unstable as the reynolds number crosses a critical value the second is to study the dynamic transition associated with the instability of the basic flow at the critical reynolds number it is proved that the type of the phase transition is determined by a parameter called transition number which is mainly determined by the reynolds number and the aspect ratio more precisely the negative positive sign of the real part of the transition number corresponds to the continuous catastrophic transition the last objective is to apply numerical experiments to examine the specific transition type for specified control parameters we show that the real part of the transition number is always negative leading to only the continuous transition

an online coupled state input parameter estimation approach for structural dynamics abstract in many practical structural applications unknown states inputs and parameters are present however most methods require one or more of these variables to be known in order to estimate the other s in this research an estimation technique which employs physical models is proposed to perform coupled state input parameter estimation in order to obtain a modeling technique which allows the estimation of a wide range of parameters in a generic fashion at a minimal computational cost even real time the use of a parametric model reduction technique is proposed the reduced model is coupled to an extended kalman filter ekf with augmented states for the unknown inputs and parameters this leads to a very efficient framework for estimation in structural dynamics problems special attention is also given to the measurement requirements in order to obtain an adequate observability of all unknown quantities and the necessity for at least one displacement level measurement is shown the proposed methodology is validated numerically and experimentally the approach is shown to be easy to tune and provides good results with different measurement methods

fundamental properties of tsallis relative entropy fundamental properties for the tsallis relative entropy in both classical and quantum systems are studied as one of our main results we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by hiai and petz the monotonicity of the quantum tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible the generalized tsallis relative entropy is defined and its subadditivity is shown by its joint convexity moreover the generalized peierls bogoliubov inequality is also proven

a two level finite element discretization of the streamfunction formulation of the stationary quasi geostrophic equations of the ocean in this paper we proposed a two level finite element discretization of the nonlinear stationary quasi geostrophic equations which model the wind driven large scale ocean circulation optimal error estimates for the two level finite element discretization were derived numerical experiments for the two level algorithm with the argyris finite element were also carried out the numerical results verified the theoretical error estimates and showed that for the appropriate scaling between the coarse and fine mesh sizes the two level algorithm significantly decreases the computational time of the standard one level algorithm

equivalence of two bochkov kuzovlev equalities in quantum two level systems we present two kinds of bochkov kuzovlev work equalities in a two level system that is described by a quantum markovian master equation one is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint we show that these two equalities are indeed equivalent importantly this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function we use a numerical model to verify these results

on uniqueness of the dynamic finite step problem in gradient dependent softening plasticity the dynamic evolution of an elastoplastic softening solid is considered a material model including in the yield function the laplacian of the plastic multiplier is used to regularize the problem the dynamic finite step problem is formulated according to a generalized mid point integration scheme space discretization is carried out by a mixed finite element technique based on generalized variables a sufficient uniqueness condition of the finite step solution is proved for a one dimensional problem also a necessary and sufficient condition is presented a simple numerical test shows the regularizing properties mesh independence of the proposed model and the positive influence of the gradient term also on the time step amplitude ensuring uniqueness of solution

well posedness for a transport equation with nonlocal velocity abstract we study a one dimensional transport equation with nonlocal velocity which was recently considered in the work of cordoba cordoba and fontelos a cordoba d cordoba m a fontelos formation of singularities for a transport equation with nonlocal velocity ann of math 2 162 3 2005 1377 1389 we show that in the subcritical and critical cases the problem is globally well posed with arbitrary initial data in h max 3 2 0 while in the supercritical case the problem is locally well posed with initial data in h 3 2 and is globally well posed under a smallness assumption some polynomial in time decay estimates are also discussed these results improve some previous results in a cordoba d cordoba m a fontelos formation of singularities for a transport equation with nonlocal velocity ann of math 2 162 3 2005 1377 1389

entropic test of quantum contextuality we study the contextuality of a three level quantum system using classical conditional entropy of measurement outcomes first we analytically construct the minimal configuration of measurements required to reveal contextuality next an entropic contextual inequality is formulated analogous to the entropic bell inequalities derived by braunstein and caves phys rev lett 61 662 1988 that must be satisfied by all noncontextual theories we find optimal measurements for violation of this inequality the approach is easily extendable to higher dimensional quantum systems and more measurements our theoretical findings can be verified in the laboratory with current technology

l2 stability for solutions of subcritical quasi geostrophic equation with large perturbations abstract this paper concerns with the asymptotic stability for the weak solution of the two dimensional dissipative subcritical quasi geostrophic equation in the class l p 0 t l q r 2 for p 2 q 2 q 1 2 it is proved that although the initial data and external force perturbations from are large every perturbed weak solution converges asymptotically to in l 2 r 2 as t as a byproduct we also obtain the weak strong uniqueness criterion of subcritical quasi geostrophic equation which improves the earlier results

the barotropic vorticity equation under forcing and dissipation bifurcations of nonsymmetric responses and multiplicity of solutions a simplified model of barotropic flow in a bounded domain has been used and stationary responses due to the balance between dissipation and external forcing have been studied the forcing as well as the domain is assumed to admit some symmetry group sufficient conditions are deduced by which a branch of nonsymmetric stationary solutions bifurcate from a symmetric one and those results are applied to a specific problem of zonally symmetric forcing in an open channel

self regularized pseudo time marching schemes for structural system identification with static measurements we explore the application of pseudo time marching schemes involving either deterministic integration or stochastic filtering to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response solutions of such non linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping an important yet inadequately understood aspect in dynamic system identification problems the usual method of least square solution is through a regularized gauss newton method gnm whose results are known to be sensitively dependent on the regularization parameter and data noise intensity finite time recursive integration of the pseudo dynamical gnm pd gnm update equation addresses the major numerical difficulty associated with the near zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration therefore we also propose a pseudo dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo dynamic ensemble kalman filter pd enkf for multiple sets of measurements involving various load cases we expedite the speed of thepd enkf by proposing an inner iteration within every time step results using the pseudo dynamic strategy obtained through pd enkf and recursive integration are compared with those from the conventional gnm which prove that the pd enkf is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small

global well posedness and finite dimensional global attractor for a 3 d planetary geostrophic viscous model in this paper we consider a three dimensional planetary geostrophic viscous model of the gyre scale mid latitude ocean we show the global existence and uniqueness of the weak and strong solutions to this model moreover we establish the existence of a nite dimensional global attractor to this dissipative evolution system c 2003 wiley periodicals inc

parameter identification in explicit structural dynamics performance of the extended kalman filter abstract an extended kalman filter ekf approach is adopted in this paper for structural systems subject to dynamic loadings to simultaneously estimate the state and calibrate constitutive parameters to pursue this aim after space and time discretizations a joint system state vector is introduced gathering nodal displacements and constitutive parameters to be identified because of the linearization of the discretized equations governing filter updates the ekf can lead to inaccurate model calibration it is shown that even though the state of the system is always followed with a high level of accuracy unsatisfactory parameter estimations can be obtained in the case of degrading strength of the structure that is in the case of softening both single degree of freedom dof and multi dof dynamic systems are analyzed to detect the possible sources of this inaccuracy

ergodic coactions with large multiplicity and monoidal equivalence of quantum groups we construct new examples of ergodic coactions of compact quantum groups in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter these examples are obtained using a bijective correspondence between certain ergodic coactions on c algebras and unitary fiber functors on the representation category of a compact quantum group we classify these unitary fiber functors on the universal orthogonal and unitary quantum groups the associated c algebras and von neumann algebras can be defined by generators and relations but are not yet well understood

jarzynski equality for quantum stochastic maps jarzynski equality and related fluctuation theorems can be formulated for various setups such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations i e for completely positive trace preserving maps which preserve the maximally mixed state we analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the jarzynski equality it contains a correction term due to nonunitality of the quantum map bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite dimensional hilbert space

global well posedness of the three dimensional viscous primitive equations of large scale ocean and atmosphere dynamics in this paper we prove the global existence and uniqueness regularity of strong solutions to the three dimensional viscous primitive equations which model large scale ocean and atmosphere dynamics 1 introduction large scale dynamics of oceans and atmosphere is governed by the primitive equations which are derived from the navier stokes equations with rotation coupled to thermodynamics and salinity diffusion transport equations which account for the buoyancy forces and stratification effects under the boussinesq approximation moreover and due to the shallowness of the oceans and the atmosphere i e the depth of the fluid layer is very small in comparison to the radius of the earth the vertical large scale motion in the oceans and the atmosphere is much smaller than the horizontal one which in turn leads to modeling the vertical motion by the hydrostatic balance as a result

waves vs particles in the atmosphere s phase space a pathway to long range forecasting thirty years ago e n lorenz provided some approximate limits to atmospheric predictability the details in space and time of atmospheric flow fields are lost after about 10 days certain gross flow features recur however after times of the order of 10 50 days giving hope for their prediction over the last two decades numerous attempts have been made to predict these recurrent features the attempts have involved on the one hand systematic improvements in numerical weather prediction by increasing the spatial resolution and physical faithfulness in the detailed models used for this prediction on the other hand theoretical attempts motivated by the same goal have involved the study of the large scale atmospheric motions9 phase space and the inhomogeneities therein these coarse graining studies have addressed observed as well as simulated atmospheric data sets two distinct approaches have been used in these studies the episodic or intermittent and the oscillatory or periodic the intermittency approach describes multiple flow or weather regimes their persistence and recurrence and the markov chain of transitions among them the periodicity approach studies intraseasonal oscillations with periods of 15 70 days and their predictability we review these two approaches particles vs waves in the quantum physics analogy alluded to in the title of this article discuss their complementarity and outline unsolved problems

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

modified constitutive relation error identification strategy for transient dynamics with corrupted data the elastic case abstract in this paper we present an identification strategy for transient dynamic tests with corrupted data and its first development for the identification of elastic properties this method is based on the modified constitutive relation error principle which was initially introduced for model updating in vibration analysis the governing principle of the method consists in splitting the equations of the problem into two groups a reliable group and an uncertain group and defining mechanical fields which verify the equations of the reliable group exactly and those of the uncertain group only approximately then these fields are used to estimate the quality of the model to be identified we tested our method on various examples and found it to be very robust with respect to high levels of perturbations furthermore we show that this good performance is due to the fact that the method takes into account all the experimental data in a single calculation and introduces a distance between the measurements and the calculation we also propose an alternative strategy dedicated to cases where there is no a priori knowledge of the perturbations

characteristic functions based on a quantum jump trajectory characteristic functions cfs provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations qmes a conventional procedure for obtaining these functions is to resort to a first principles approach namely the evolution equations of the cfs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system however the qmes can be unraveled by a quantum jump trajectory thermodynamic quantities such as the heat work and entropy production can be well defined along a trajectory hence on the basis of the notion of a trajectory can we straightforwardly derive these cfs e g their evolution equations this is essential to establish the self contained stochastic thermodynamics of a qme in this paper we show that it is indeed plausible and also simple particularly these equations are fully consistent with those obtained by the first principles method our results have practical significance they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments

unital quantum channels convex structure and revivals of birkhoff s theorem the set of doubly stochastic quantum channels and its subset of mixtures of unitaries are investigated we provide a detailed analysis of their structure together with computable criteria for the separation of the two sets when applied to o d covariant channels this leads to a complete characterization and reveals a remarkable feature instances of channels which are not in the convex hull of unitaries can become elements of this set by either taking two copies of them or supplementing with a completely depolarizing channel these scenarios imply that a channel whose noise initially resists any environment assisted attempt of correction can become perfectly correctable

derivation of quantum work equalities using a quantum feynman kac formula on the basis of a quantum mechanical analog of the famous feynman kac formula we present a method to derive nonequilibrium work equalities for isolated quantum systems which include the jarzynski equality and bochkov kuzovlev equality compared with other methods in the literature our method shows a higher similarity in form to the method deriving the fluctuation relations in the classical systems

information theoretical properties of tsallis entropies a chain rule and a subadditivity for the entropy of type which is one of the nonadditive entropies were derived by daroczy in this paper we study the further relations among tsallis type entropies which are typical nonadditive entropies the chain rule is generalized by showing it for tsallis relative entropy and the nonadditive entropy we show some inequalities related to tsallis entropies especially the strong subadditivity for tsallis type entropies and the subadditivity for the nonadditive entropies the subadditivity and the strong subadditivity naturally lead to define tsallis mutual entropy and tsallis conditional mutual entropy respectively and then we show again chain rules for tsallis mutual entropies we give properties of entropic distances in terms of tsallis entropies finally we show parametrically extended results based on information theory