long time evolution of wavefronts in random media this work studies the evolution of the front of an impulsive plane wave in a layered random medium a general second order hyperbolic equation with an inhomogeneous plane wave solution in a frame moving with random propagation speed is considered in this frame it takes the form of a coupled system of ordinary differential equations along characteristics for the propagation modes the author shows that in the asymptotic limit in which the amplitude of random inhomogeneities decreases but the distance at which the pulse is observed increases the leading part of the pulse the wavefront stabilizes to a deterministic waveform this waveform depends on the statistical properties of the medium and the initial pulse only and it is explicitly calculable the theory is applied to the elastic wave equations in a two dimensional medium

brief paper stochastic maximum principle in the mean field controls in buckdahn djehiche li and peng 2009 the authors obtained mean field backward stochastic differential equations bsdes in a natural way as a limit of some highly dimensional system of forward and backward sdes corresponding to a great number of particles or agents the objective of the present paper is to deepen the investigation of such mean field bsdes by studying their stochastic maximum principle this paper studies the stochastic maximum principle smp for mean field controls which is different from the classical ones this paper deduces an smp in integral form and it also gets under additional assumptions necessary conditions as well as sufficient conditions for the optimality of a control as an application this paper studies a linear quadratic stochastic control problem of mean field type

optimization criteria bounds and efficiencies of heat engines the efficiency of four different and representative models of heat engines under maximum conditions for a figure of merit representing a compromise between useful energy and lost energy the ensuremath omega criterion is investigated and compared with previous results for the same models where the efficiency is considered at maximum power conditions it is shown that the maximum ensuremath omega regime is more efficient and additionally that the resulting efficiencies present a similar behavior for each performance regime we obtain explicit equations accounting for lower and upper bounds the optimization of refrigeration devices is far from being as clear as heat engines and some remarks on it are finally considered

finding adapted solutions of forward backward stochastic differential equations method of continuation the notion of bridge is introduced for systems of coupled forward backward stochastic differential equations fbsdes for short this notion helps us to unify the method of continuation in finding adapted solutions to such fbsdes over any finite time durations it is proved that if two fbsdes are linked by a bridge then they have the same unique solvability consequently by constructing appropriate bridges we obtain several classes of uniquely solvable fbsdes

solution of forward backward stochastic differential equations in this paper we study the existence and uniqueness of the solution to forward backward stochastic differential equations without the nondegeneracy condition for the forward equation under a certain monotonicity condition we prove the existence and uniqueness of the solution to forward backward stochastic differential equations

estimation of pulse shaping for well logs a wavelet propagating in a finely layered lossless medium is subject to apparent attenuation that changes its shape can a sonic log be used to characterize this change i show that numerical simulations with the well log as medium give an apparent attenuation or diffusion of the pulse that is very different from the attenuation in the real medium this is due to the smoothing effect of the well log tool based on a version of the o doherty anstey approximation i derive an expression that reveals the role of the tool using a sonic log i verify the theory and show how tool effects can be mitigated by deconvolution i also propose a two scale stochastic model for the sonic log and a procedure for estimation of its parameters one application of sonic logs is to quantify apparent attenuation and in this context my results are important

mean field stochastic h 2 h control with delay the finite horizon h 2 h control problem of mean field type for delayed stochastic systems is considered in this paper firstly we derive a sufficient mean field generalised stochastic bounded

entropy production estimation with optimal current entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems according to the thermodynamic uncertainty relation we propose a deterministic method to estimate the entropy production from a single trajectory of system states we explicitly and approximately compute an optimal current that yields the tightest lower bound using predetermined basis currents notably the obtained tightest lower bound is intimately related to the multidimensional thermodynamic uncertainty relation by proving the saturation of the thermodynamic uncertainty relation in the short time limit the exact estimate of the entropy production can be obtained for overdamped langevin systems irrespective of the underlying dynamics for markov jump processes because the attainability of the thermodynamic uncertainty relation is not theoretically ensured the proposed method provides the tightest lower bound for the entropy production when entropy production is the optimal current a more accurate estimate can be further obtained using the integral fluctuation theorem we illustrate the proposed method using three systems a four state markov chain a periodically driven particle and a multiple bead spring model the estimated results in all examples empirically verify the effectiveness and efficiency of the proposed method

frequency content of randomly scattered signals the statistical properties of acoustic signals reflected by a randomly layered medium are analyzed when a pulsed spherical wave issuing from a point source is incident upon it the asymptotic analy

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

an optimal control problem for mean field forward backward stochastic differential equation with noisy observation abstract this article is concerned with an optimal control problem derived by mean field forward backward stochastic differential equation with noisy observation where the drift coefficients of the state equation and the observation equation are linear with respect to the state and its expectation the control problem is different from the existing literature concerning optimal control for mean field stochastic systems and has more applications in mathematical finance e g asset liability management problem with recursive utility systematic risk model using a backward separation method with a decomposition technique two optimality conditions along with two coupled forward backward optimal filters are derived linear quadratic optimal control problems for mean field forward backward stochastic differential equations are studied

noninvasive measurement of dissipation in colloidal systems according to harada and sasa phys rev lett 95 130602 2005 heat production generated in a nonequilibrium steady state can be inferred from measuring response and correlation functions in many colloidal systems however it is a nontrivial task to determine response functions whereas details about spatial steady state trajectories are easily accessible using a simple conditional averaging procedure we show how this fact can be exploited to reliably evaluate average heat production we test this method using brownian dynamics simulations and apply it to experimental data of an interacting driven colloidal system

mean field backward stochastic differential equations a limit approach mathematical mean field approaches play an important role in different fields of physics and chemistry but have found in recent works also their application in economics finance and game theory the objective of our paper is to investigate a special mean field problem in a purely stochastic approach for the solution y z of a mean field backward stochastic differential equation driven by a forward stochastic differential of mckean vlasov type with solution x we study a special approximation by the solution x n y n z n of some decoupled forward backward equation which coefficients are governed by n independent copies of x n y n z n we show that the convergence speed of this approximation is of order 1 root n moreover our special choice of the approximation allows to characterize the limit behavior of root n x n x y n y z n z we prove that this triplet converges in law to the solution of some forward backward stochastic differential equation of mean field type which is not only governed by a brownian motion but also by an independent gaussian field

optimality variational principle for controlled forward backward stochastic differential equations with mixed initial terminal conditions an optimal control problem for general coupled forward backward stochastic differential equations fbsdes with mixed initial terminal conditions is considered the control domain is not assumed to be convex and the control appears in the diffusion coefficient of the forward equation necessary conditions of pontraygin s type for the optimal controls are derived by means of spike variation techniques

physical origins of entropy production free energy dissipation and their mathematical representations a unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master equations is presented as generalizations of isothermal entropy and free energy two functions of state play central roles the gibbs entropy s and the relative entropy f which are related via the stationary distribution of the stochastic dynamics s satisfies the fundamental entropy balance equation ds dt e p ensuremath h d t with entropy production rate e p ensuremath ge 0 and heat dissipation rate h d while df dt ensuremath f d ensuremath le 0 for closed systems that satisfy detailed balance t e p t f d t for open systems one has t e p t f d t q hk t where the housekeeping heat q hk ensuremath ge 0 was first introduced in the phenomenological nonequilibrium steady state thermodynamics put forward by oono and paniconi q hk represents the irreversible work done by the surrounding to the system that is kept away from reaching equilibrium hence entropy production e p consists of free energy dissipation associated with spontaneous relaxation i e self organization f d and active energy pumping that sustains the open system q hk the amount of excess heat involved in the relaxation q ex h d ensuremath q hk f d ensuremath t ds dt two kinds of irreversibility and the meaning of the arrow of time emerge quasistationary processes adiabaticity and maximum principle for entropy are also generalized to nonequilibrium settings

three level laser heat engine at optimal performance with ecological function although classical and quantum heat engines work on entirely different fundamental principles there is an underlying similarity for instance the form of efficiency at optimal performance may be similar for both types of engines in this work we study a three level laser quantum heat engine operating at maximum ecological function ef which represents a compromise between the power output and the loss of power due to entropy production we present numerical as well as analytic results for the global and local optimization of our laser engine in different operational regimes particularly we observe that in low temperature regimes the three level laser heat engine can be mapped to feynman s ratchet and pawl model a steady state classical heat engine then we derive analytic expressions for efficiency under the assumptions of strong matter field coupling and high bath temperatures upper and lower bounds on the efficiency exist in case of extreme asymmetric dissipation when the ratio of system bath coupling constants at the hot and the cold contacts respectively approaches zero or infinity these bounds have been established previously for various classical models of carnot like engines further for weak or intermediate matter field coupling in the high temperature limit we derive some new bounds on the efficiency of the engine we conclude that while the engine produces at least 75 of the power output as compared with the maximum power conditions the fractional loss of power is appreciably low in case of the engine operating at maximum ef thus making this objective function relevant from an environmental point of view

a maximum principle for fully coupled stochastic control systems of mean field type abstract the present paper considers an optimal control problem for fully coupled forward backward stochastic differential equations fbsdes of mean field type in the case of controlled diffusion coefficient moreover the control domain is not assumed to be convex by virtue of a reduction method we establish the necessary optimality conditions of pontryagin s type as an application a linear quadratic stochastic control problem is studied

a general maximum principle for optimal control of forward backward stochastic systems abstract a general maximum principle for optimal control problems derived by forward backward stochastic systems is established where control domains are non convex and forward diffusion coefficients explicitly depend on control variables these optimal control problems have broad applications in mathematical finance and economics such as the recursive mean variance portfolio choice problems the maximum principle is applied to study a forward backward linear quadratic optimal control problem with a non convex control domain an optimal solution is obtained

the risk sensitive maximum principle for controlled forward backward stochastic differential equations abstract in this paper we consider the risk sensitive optimal control problem for forward backward stochastic differential equations fbsdes we consider two different cases case 1 the drift and diffusion terms of the forward part are independent of the backward part not fully coupled fbsde and the running cost does not include the backward part case 2 the fully coupled fbsde with terminal and initial costs in both cases the risk sensitive objective functional is considered the corresponding control domain is not necessarily convex and the diffusion term of the forward part depends on control and state variables in both cases by using the nonlinear transformations of the equivalent risk neutral problems we obtain two different risk sensitive maximum principles which are characterized in terms of the variational inequalities we show that the risk sensitive maximum principle of case 1 consists of the two coupled adjoint equations with an additional scalar adjoint equation which are backward stochastic differential equations bsdes the risk sensitive maximum principle of case 2 consists of the two coupled adjoint equations which are coupled fbsdes with an additional scalar adjoint equation and optimality conditions in both cases the additional scalar adjoint equations are bsdes which are induced due to the nonlinear transformations of the adjoint processes in the equivalent risk neutral problems through the application of results we consider the linear quadratic risk sensitive optimal control problem for the linear fbsde and by using the risk sensitive maximum principle of case 1 we characterize an explicit optimal solution

optimal control of mean field jump diffusion systems with noisy memory abstractthis paper is concerned with an optimal control problem under mean field jump diffusion systems with delay and noisy memory first we derive necessary and sufficient maximum principles using malliavin calculus technique meanwhile we introduce a new mean field backward stochastic differential equation as the adjoint equation which involves not only partial derivatives of the hamiltonian function but also their malliavin derivatives then applying a reduction of the noisy memory dynamics to a two dimensional discrete delay optimal control problem we establish the second set of necessary and sufficient maximum principles under partial information moreover a natural link between the above two approaches is established via the adjoint equations finally we apply our theoretical results to study a mean field linear quadratic optimal control problem

efficiency bounds of molecular motors under a trade off figure of merit abstract on the basis of the theory of irreversible thermodynamics and an elementary model of the molecular motors converting chemical energy by atp hydrolysis to mechanical work exerted against an external force the efficiencies of the molecular motors at two different optimization configurations for trade off figure of merit representing a best compromise between the useful energy and the lost energy are calculated the upper and lower bounds for the efficiency at two different optimization configurations are determined it is found that the optimal efficiencies at the two different optimization configurations are always larger than 1 2