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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Minkowski problem in Gaussian probability space
高斯概率空间 闵可夫斯基问题 广义相对论
2023/5/6
The classical Minkowski problem, which asks for the characterization of surface area measure in Euclidean space with Lebesgue measure, largely motivated the development of elliptic PDEs throughout the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convexity, Uniqueness, and Stability of the Regular Shock Reflection-diffraction Problem
规则冲击 反射衍射问题 凸性 唯一性 稳定性
2023/4/17
We will talk about our recent results on the convexity, uniqueness, and stability of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The appr...
Physics of laser frequency combs sheds light on nature’s problem-solving skills（图）
Physics laser frequency combs sheds light problem-solving skills
2019/10/23
Nature has a way of finding optimal solutions to complex problems. For example, despite billions of ways for a single protein to fold, proteins always fold in a way that minimizes potential energy. Sl...
Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment
Spin quantum interactive microcosmic spin micro rotation magnetic particles low-energy properties model
2014/12/23
We consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model desc...
Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome
Monte carlo thick line diagram unknown functions
2014/12/20
We introduce a Monte Carlo scheme for sampling a bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo ...
Bold diagrammatic Monte Carlo: A generic sign-problem tolerant technique for polaron models and possibly interacting many-body problems
Monte carlo feynman diagrams reforming particles breeding the particles
2014/12/20
We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy, which are self-consistently expressed in terms of renormalized particle propagators. This approach i...
Fermi-polaron problem: Diagrammatic Monte Carlo method for divergent sign-alternating series
Diagram to monte carlo method Fermi gas particle condensed matter
2014/12/20
We use the diagrammatic Monte Carlo approach to solve the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles. Our solution is important for understandin...
Solving the inverse problem of high numerical aperture focusing using Slepian-type vector fields
High numerical aperture focusing Vector diffraction theory Inverse problem Slepian’s concentration problem
2012/5/29
A technique using vector Slepian harmonics and multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or ...
Traveling Baseball Players' Problem in Korea
Monte-Carlo simulation optimization traveling salesman problem traveling tournament prob-lem sports tournament baseball league
2012/5/29
We study the so-called the traveling tournament problem (TTP), to find an optimal tournament schedule. Differently from the original TTP, in which the total travel distance of all the participants is ...
Complex-Dynamical Solution to Many-Body Interaction Problem and Its Applications in Fundamental Physics
Complex-Dynamical Solution Many-Body Interaction Problem Fundamental Physics quantum mechanics
2012/4/27
We review the recently proposed unreduced, complex-dynamical solution to many-body problem with arbitrary interaction and its application to unified solution of fundamental problems, including foundat...
Complex-Dynamical Solution to Many-Body Interaction Problem and Its Applications in Fundamental Physics
Complex-Dynamical Solution Many-Body Interaction Problem Fundamental Physics General Physics
2012/4/25
We review the recently proposed unreduced, complex-dynamical solution to many-body problem with arbitrary interaction and its application to unified solution of fundamental problems, including foundat...
An exact solution of the moving boundary problem for the relativistic plasma expansion in a dipole magnetic field
exact solution of the moving boundary problem relativistic plasma expansion dipole magnetic field Plasma Physics
2012/4/19
An exact analytic solution is obtained for a uniformly expanding, neutral, highly conducting plasma sphere in an external dipole magnetic field with an arbitrary orientation of the dipole moment in th...
Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid
Stokes’ first problem viscoelastic generalized second grade fluid Integral-balance solution Deborah number
2011/9/21
Abstract: Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes' first problem of a viscoelastic generalized second grade fluid has been develo...
Method of oscillation and spectral problem for four-order differential operator with self-similar weight
Method of oscillation spectral problem self-similar weight
2011/9/20
Abstract: Self-adjoint boundary problems for the equation $y^{(4)}-\lambda\rho y=0$ with generalized derivative $\rho\in W_2^{-1}[0,1]$ of self-similar Cantor type function as a weight are considered....
A solution of the non-uniqueness problem of the Dirac Hamiltonian and energy operators
non-uniqueness problem Dirac Hamiltonian energy operators General Relativity and Quantum Cosmology
2011/10/9
Abstract: In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from r...