We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense. 相似文献
In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.
We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of
times, the k-level has subquadratic (O(n2-1/2s) complexity. This answers one of the main open problems from the author’s previous paper [DCG 29, 375-393 (2003)],
which provided a weaker upper bound for a
restricted class of curves only (graphs of degree-s polynomials).
When combined with existing tools (cutting curves, sampling, etc.),
the new idea generates a slew of improved k-level results for
most of the curve families studied earlier, including a
near-O(n3/2 bound for parabolas. 相似文献
Methods for obtaining alkylindoles, excluding the Fischer synthesis and direct alkylation, developed during the last 15 years are correlated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1155–1172, September, 1987. 相似文献
The ultraviolet band systemsA1Π-X1Σ+ of P14N and P15N were excited in an electrodeless tube containing traces of phosphorus specpure nitrogen and neon using a microwave discharge
(2450 MHz). Bands of the isotopic species, P15N, were obtained using15N2 enriched to 95.5%. Rotational analyses of eleven bands of P14N and sixteen bands of P15N were carried out. Three perturbing statese3Σ−,d3Δ andb3Π, arising from the lower valence configurations were identified from the observed perturbations in thev′=0–4 levels of theA1Π state. Deperturbation studies led to the determination of molecular constants of the perturbing states. Vibrational assignments
of the perturbing states were made from isotope shift studies. 相似文献
The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents anO(n2) time sequential algorithm and anO(n2/p+logn) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, wherep andn represent respectively the number of processors and the number of vertices of the circular-arc graph. 相似文献
We develop a theory of the magnetic-zenith effect (MZE) observed upon the ionosphere modification by powerful radio waves.
The dependences of MZE on main parameters, such as the magnetic-field inclination angle, pump-wave frequency and power, and
angular width of HF beam are obtained. The optimal elevation angle of pump-wave beam is predicted.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 772–787, September 2005. 相似文献
The influence of the substrate temperature Tsub (20–360°C) and the oxygen pressure P(O2) (5 × 10−3−0.13 Pa) in an evaporation chamber on the structure and phase composition of films prepared through laser sputtering of a vanadium target is investigated by electron diffraction and in situ transmission electron microscopy (with the use of the bend extinction contour technique for determining the bending of the crystal lattice). It is demonstrated that the oxygen content in the films increases with an increase in the oxygen pressure P(O2) at a fixed substrate temperature Tsub and decreases with an increase in the substrate temperature Tsub at a fixed oxygen pressure P(O2). The conditions responsible for the formation and composition of the crystalline (VO0.9) and amorphous (V2O3) phases in the films are determined. It is established that the phase composition of the film depends on the angle of condensation of the vapor-plasma flow. The crystallization of the V2O3 amorphous phase is accompanied by an increase in the density by 9.2%. It is revealed that the V2O3 spherulites growing in the amorphous film have a bent crystal lattice. The bending of the crystal lattice can be as large as ∼42 deg/μm.