Equilibrium Configurations of Tripolar Charges

It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic combinatoric rule remains essentially the same on different levels of the hierarchy, thus leading to a pattern of resemblance between different levels. The number of primitive charges in each structure is determined by the symmetry of the combined effective potential of this structure. The outlined scheme can serve as a framework for building a model of composite fundamental fermions.     

The Quantum N-Body Problem and the Auxiliary Field Method

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and applied to the case of baryons in the large-N _c limit.     

Orbital Divergence and Relaxation in the Gravitational N-Body Problem

One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical gravitational N-body problem. The application we have in mind is to old stellar systems such as globular star clusters, where N10⁶, and so we concentrate on spherical, centrally concentrated systems with total energy E<0. Hitherto no connection has been made between the time scale for divergence (denoted here by t _e ) and the time scale on which the energies of the particles evolve because of two-body encounters (i.e., the two-body relaxation time scale, t _r ), even though both may be calculated by similar considerations. In this paper we give a simplified model showing that divergence in phase space is initially roughly exponential, on a timescale proportional to the crossing time (defined as a mean time for a star to cross from one side of the system to another). In this phase t _e <<t _r , if N is not too small (i.e., N30). After several e-folding times, the model shows that the divergence slows down. Thereafter the divergence (measured by the energies of the bodies) varies with time as t ^1/2, on a timescale nearly proportional to the familiar two-body relaxation timescale, i.e., t _e t _r in this phase. These conclusions are illustrated by numerical results.     

Equilibrium Plasma Configurations in the Vicinity of the Generic Point

The structure of an arbitrary equilibrium plasma configuration in an external potential field and a potential force magnetic field are studied in the plane geometry.     

Electron-Vibrational Interaction and Equilibrium Configurations of the Hydrogen Peroxide Molecule

We show that electron-vibrational interaction (Renner effect) in the model of linear configuration of the hydrogen peroxide molecule leads to removal of degeneracy of the electronic state and is the determining factor for the existence of two dissimilar nonplanar equilibrium symmetrically equivalent configurations.     

The Quantum N-Body Problem and the Auxiliary Field Method: New Developments

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and a connection is presented between the method and the generalized virial theorem. The procedure is applied to the case of baryons in the large-N _c limit.     

Equilibrium Configurations of Lipid Bilayer Membranes and Carbon Nanostructures

The present article concerns the continuum modelling of the mechanical behaviour and equilibrium shapes of two types of nano-scale objects: fluid lipid bilayer membranes and carbon nanostructures. A unified continuum model is used to handle four different case studies. Two of them consist in representing in analytic form cylindrical and axisymmetric equilibrium configurations of single-wall carbon nanotubes and fluid lipid bilayer membranes subjected to uniform hydrostatic pressure. The third one is concerned with determination of possible shapes of junctions between a single-wall carbon nanotube and a flat graphene sheet or another single-wall carbon nanotube. The last one deals with the mechanical behaviour of closed fluid lipid bilayer membranes (vesicles) adhering onto a flat homogeneous rigid substrate subjected to micro-injection and uniform hydrostatic pressure.     

The Weyl Tensor and Equilibrium Configurations of Self-Gravitating Fluids

It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with respect to its value in the state of equilibrium (or quasi-equilibrium).     

On Equilibrium Configurations in Continuum Mechanics of Structural Defects

We consider the determination of the theory by a second order tensor field g_ik and affinity Γ^f_ik. By variational principle for Einstein-Hilbert Lagrangian solid state equilibrium positions of the ideal and real crystal will be described. On account of external Galilei-invariance this theory affords an invariant three dimensional geometry at most being able to produce a stable static equilibrium of defects. The motion of defects is related to the theory of invariants of the internal group of field equations produced by this theory in strong analogy to Maxwell's electrodynamics. The elastic ether concept for the theory of light affords the idea of a gauge field approximation of continuum mechanics fitting linearized Einstein-Hilbert Lagrangian approach. The stress and strain space duality has to be understood on this background.     

Integrable Properties Associated with a Discrete Three-by-Three Matrix Spectral Problem

Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that the hierarchy possesses a HamiItonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.     

Integrable Properties Associated with a Discrete Three-by-Three Matrix Spectral Problem

Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that thehierarchy possesses a Hamiltonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.     

Equilibrium Properties of H-Plasma

The equilibrium properties of the dense semiclassical hydrogen plasma are investigated by chain of Bogolyubov equations. The pseudopotential model, taking into account both short-range quantum-mechanical effects and long-range many-particle screening ones, is proposed. The equation of state of hydrogen plasma is investigated.     

Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

This paper studies numerically the photogravitational version of the restricted four-body problem, where an infinitesimal particle is moving under the gravitational attraction and radiation pressure of three bodies much bigger than the particle, the primaries. The fourth body does not affect the motion of the three bodies. These bodies are always at the vertices of an equilateral triangle (Lagrange configuration). We consider all the primary bodies (m ₁, m ₂, m ₃) as radiation sources with radiation factors of the two bodies (m ₂ and m ₃) equal. In this paper we suppose the masses of the three primary bodies are equal. It is found that the involved parameters influenced the positions of the equilibrium points. The linear stability of the relative equilibrium solutions is also studied and all these points are unstable.     

Polynomials Satisfying Functional and Differential Equations and Diophantine Properties of Their Zeros

By investigating the behavior of two solvable isochronous N-body problems in the immediate vicinity of their equilibria, functional equations satisfied by the para-Jacobi polynomial ${p_{N} \left(0, 1; \gamma; x \right)}$ and by the Jacobi polynomial ${P_{N}^{\left(-N-1,-N-1 \right)} \left(x \right)}$ (or, equivalently, by the Gegenbauer polynomial ${C_{N}^{-N-1/2}\left( x \right) }$ ) are identified, as well as Diophantine properties of the zeros and coefficients of these polynomials.     

General Decomposition of Radial Functions on Rn and Applications to N-Body Quantum Systems

We present a generalization of the Fefferman–de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions V on Rⁿ going to zero at infinity. This generalized decomposition can be used to extend previous results on N-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application, we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.     

Equilibrium and Non-equilibrium Properties of Superfluids and Superconductors

We review some rigorous results on the equilibrium and non-equilibrium properties of superfluids and superconductors.     

高精度环形谱仪等时性模式的闭轨校正模拟

高精度环形谱仪（SRing）是HIAF装置的重要组成部分,闭轨校正设计是该同步加速器设计的关键部分。由于等时性模式（γ_t=1.43）线性光学水平β函数很大,磁铁场误差及安装误差会引起较大的闭轨畸变,并导致线性光学发生变化。模拟过程采用奇异值分解（SVD）算法,通过多次计算响应矩阵并计算校正铁校正量实现闭轨校正。同时考虑BPM误差的影响,并通过减少特征值使用个数降低校正铁校正量。校正后全环最大闭轨小于0.8 mm,线性光学也得到明显优化。