Searcharxiv⌕ Search

arXiv subjects

Xu Zhang

Publications and source records attributed to Xu Zhang.

521 records · Page 29Linked to original sources
arXiv2013

Four Kahler Moduli Stabilisation in type IIB Orientifolds with K3-fibred Calabi-Yau threefold compactification

We present a concrete and consistent procedure to generate one kind of non-perturbative superpotential, including the gaugino condensation corrections and poly-instanton corrections, in type IIB orientifold compactification with four Kahler Moduli. Then we use this kind of superpotential as well as the alphaprime-corrections to Kahler potential to fix all of the four Kahler moduli on a general Calabi-Yau manifold with typical K3-fibred volume form. In our construction, the considered Calabi-Yau threefolds are K3-fibred and admit at least one del Pezzo surface and one W-surface. Searching through all existing four dimensional reflexive lattice polytopes, we find 23 of them fulfilling all the requirements.

hep-th↗
arXiv2012

General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

The main purpose of this paper is to give a solution to a long-standing unsolved problem in stochastic control theory, i.e., to establish the Pontryagin-type maximum principle for optimal controls of general infinite dimensional nonlinear stochastic evolution equations. Both drift and diffusion terms can contain the control variables, and the control domains are allowed to be nonconvex. The key to reach it is to provide a suitable formulation of operator-valued backward stochastic evolution equations (BSEEs for short), as well as a way to define their solutions. Besides, both vector-valued and operator-valued BSEEs, with solutions in the sense of transposition, are studied. As a crucial preliminary, some weakly sequential Banach-Alaoglu-type theorems are established for uniformly bounded linear operators between Banach spaces.

math.OC↗
arXiv2012

Global Uniqueness for an Inverse Stochastic Hyperbolic Equation with Three Unknowns

This paper is addressed to an inverse stochastic hyperbolic equation with three unknowns, i.e., a source term, an initial displacement and an initial velocity. The global uniqueness is proved by a new global Carleman estimate for the stochastic hyperbolic equation. It is found that both the formulation of stochastic inverse problems and the tools to solve them differ considerably from their deterministic counterpart.

math-ph↗
arXiv2012

L1-norm minimization for quaternion signals

The l1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l1-norm minimization for quaternion signals by converting it to second-order cone programming. An application example of the proposed algorithm is also given for practical guidelines of perfect recovery of quaternion signals. The proposed algorithm may find its potential application when CS theory meets the quaternion signal processing.

math.NA↗
arXiv2011

Well-posedness of Backward Stochastic Differential Equations with General Filtration

This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a new notion of solution, i.e., the transposition solution, which coincides with the usual strong solution when the filtration is natural but it is more flexible for the general filtration than the existing notion of solutions. A comparison theorem for transposition solutions is also presented.

math.PR↗
arXiv2011

The Theory of Stochastic Pseudo-differential Operators and Its Applications, I

The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential operators and prove their fundamental properties. Also, we present the boundedness theory, invertibility of stochastic elliptic operators and the Garding inequality. Moreover, as an application of the theory of stochastic pseudo-differential operators, we give a Calderon-type uniqueness theorem on the Cauchy problem of stochastic partial differential equations. The proof of the uniqueness theorem is based on a new Carleman-type estimate, which is adapted to the stochastic setting.

math.AP↗
arXiv2010

Hyperbolicity of the invariant sets for the real polynomial maps

It is well known that for $a>4$, the dynamical behaviors of the logistic map $f_a(x)=ax(1-x)$ on the maximal invariant compact set are "simple" which could be clearly explained by the theories of hyperbolic dynamics and symbolic dynamics. Is it possible that similar phenomena could be observed in general real polynomial maps? In this paper, we study this problem by investigating the real polynomial map $f_a(x)=ag(x)$, where $a$ is a parameter, and $g$ is a real-coefficient polynomial, which has at least two different real zeros or only one real zero.

math.DS↗
arXiv2010

Calderon-Type Uniqueness Theorem for Stochastic Partial Differential Equations

In this Note, we present a Calderón-type uniqueness theorem on the Cauchy problem of stochastic partial differential equations. To this aim, we introduce the concept of stochastic pseudo-differential operators, and establish their boundedness and other fundamental properties. The proof of our uniqueness theorem is based on a new Carleman-type estimate.

math.PR↗
arXiv2010

Weak Maximum Principle for Strongly Coupled Elliptic Differential Systems

A classical counterexample due to E. De Giorgi, shows that the weak maximum principle does not remain true for general linear elliptic differential systems. After that, there are some efforts to establish the weak maximum principle for special elliptic differential systems, but the existing works are addressing only the cases of weakly coupled systems, or almost-diagonal systems, or even some systems coupling in various lower order terms. In this paper, by contrast, we present maximum modulus estimates for weak solutions to two classes of coupled linear elliptic differential systems with different principal parts, under considerably mild and physically reasonable assumptions. The systems under consideration are strongly coupled in the second order terms and other lower order terms, without restrictions on the size of ratios of the different principal part coefficients, or on the number of equations and space variables.

math.AP↗
arXiv2010

Representation of Itô Integrals by Lebesgue/Bochner Integrals

In [22], it was proved that as long as the integrand has certain properties, the corresponding Itô integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later can be regarded as a variant of the classical Riesz Representation Theorem, and therefore it will be useful in studying other problems. Some remarkable consequences are presented as well, including a reasonable definition of exact controllability for stochastic differential equations and a condition which implies a Black-Scholes market to be complete.

math.PR↗
arXiv2010

A unified controllability/observability theory for some stochastic and deterministic partial differential equations

The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial analytic tool is a class of fundamental weighted identities for stochastic/deterministic partial differential operators, via which one can derive the desired global Carleman estimates. This method can also give a unified treatment of the stabilization, global unique continuation, and inverse problems for some stochastic/deterministic partial differential equations.

math.OC↗
arXiv2009

Quantum Mechanical Simulations of Nanoindentation of Al Thin Film

QCDFT is a multiscale modeling approach that can simulate multi-million atoms effectively via density functional theory (DFT). The method is based on the framework of quasicontinuum (QC) approach with DFT as its sole energetics formulation. The local QC energy is calculated by DFT with Cauchy-Born hypothesis and the nonlocal QC energy is determined by a self-consistent embedding approach, which couples nonlocal QC atoms to the vertices of the finite-elements at the local QC region. The QCDFT method is applied to a nanoindentation study of an Al thin film in the presence and absence of Mg impurities. The results show that the randomly distributed Mg impurities can significantly increase the ideal and yield strength of the Al thin film.

cond-mat.mes-hall↗
arXiv2009

Structure, mechanical and thermodynamic stability of vacancy clusters in Cu

The atomic structure, mechanical and thermodynamic stability of vacancy clusters in Cu are studied by atomistic simulations. The most stable atomic configuration of small vacancy clusters is determined. The mechanical stability of the vacancy clusters is examined by applying uniaxial and volumetric tensile strain to the system. The yield stress and yield strain of the system are significantly reduced comparing to the prefect lattice. The dependence of vacancy formation and binding energy as a function of strain is explored and can be understood from the liquid-drop model. We find that the formation energy of the vacancy clusters decreases monotonically as a function of the uniaxial strain, while the formation energy increases first then decreases under the volumetric tensile strain. The thermodynamic stability of the vacancy clusters is analyzed by calculating the Gibbs free binding energy and the total probability of dissociation of the vacancy clusters at 300 K and 900 K under uniaxial and volumetric strains. We find that although most of the vacancy clusters appear to be thermodynamically stable, some of the immediate sized clusters have high probability of dissociation into smaller clusters.

cond-mat.mtrl-sci↗
arXiv2009

Remarks on the Controllability of Some Quasilinear Equations

In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local controllability problem of quasilinear time-reversible evolution equations, which is based on a new unbounded perturbation technique. It is also worthy to mention that the technique we develop can also be applied to other problems for quasilinear equations, say local existence, stabilization, etc.

math.OC↗
arXiv2007

Carleman and Observability Estimates for Stochastic Wave Equations

Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for stochastic wave equations with non-smooth lower order terms. Moreover, the observability constant is estimated by an explicit function of the norm of the involved coefficients in the equation.

math.AP↗
arXiv2006

Unique Continuation for Stochastic Parabolic Equations

This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the the unique continuation problem for deterministic equations do not work. Our method is based on a suitable partial Holmgren coordinate transform and a stochastic version of Carleman-type estimate.

math.AP↗