Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom

This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns perturbations of the uncoupled system consisting of the simple pendulum and the harmonic oscillator. We show that small coupling perturbations with, possibly, the addition of positive and negative damping breaks the integrability by introducing horseshoes into the dynamics.Research partially supported by ARO Contract DAAG-29-79-C-0086 and by NSF Grants ENG 78-02891 and MCS-78-06718     

Crossdocking—JIT scheduling with time windows

In this paper, we study a problem central to crossdocking that aims to eliminate or minimize storage and order picking activity using JIT scheduling. The problem is modelled naturally as a machine scheduling problem. As the problem is NP-hard, and for real-time applications, we designed and implemented two heuristics. The first uses Squeaky Wheel Optimization embedded in a Genetic Algorithm and the second uses Linear Programming within a Genetic Algorithm. Both heuristics offer good solutions in experiments where comparisons are made with the CPLEX solver.     

Linearization of class C for contractions on Banach spaces

In this work we prove a C¹-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.     

Real

The famous problem involves applying two maps: and to positive integers. If is even, one applies , if it is odd, one applies . The conjecture states that each trajectory of the system arrives to the periodic orbit . In this paper, instead of choosing each time which map to apply, we allow ourselves more freedom and apply both and independently of . That is, we consider the action of the free semigroup with generators and on the space of positive real numbers. We prove that this action is minimal (each trajectory is dense) and that the periodic points are dense. Moreover, we give a full characterization of the group of transformations of the real line generated by and .

     

Exact solution of a boundary value problem describing the uniform cylindrical or spherical piston motion

In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary conditions at the shock and at the piston. The results obtained from the analytic solutions justify numerical solution and the approximate solution of Lighthill [1]. We find that although the approximate solution of Lighthill [1] gives remarkably good numerical results, the analytic form of that solution is not mathematically satisfactory. We also find that in case of spherical piston motion Lighthill’s [1] solution differs significantly from that of our analytic and numerical solutions. We use Pade′ approximation to extend the radius of convergence of the series solution. We also carry out some local analysis at the boundary to obtain some singular solutions.     

Characterization of silicon nanowires grown on silicon, stainless steel and indium tin oxide substrates

Silicon nanowires (SiNWs) have been grown on crystalline silicon (Si), indium tin oxide (ITO) and stainless steel (SS) substrates using a gold catalyst coating with a thickness of 200 nm via pulsed plasma-enhanced chemical vapor deposition (PPECVD). Their morphological, mineralogical and surface characteristics have been investigated using scanning electron microscopy (SEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and Raman analysis. SiNWs growth is accompanied by oxidation, thus yielding partially (SiO _x ) and fully oxidized (SiO₂) Si sheaths. The mean diameters of these SiNWs range from 140 to 185 nm. Si with (111) and (220) planes exists in SiNWs grown on all three substrates while Si with a (311) plane is detected only for Si and ITO substrates. Computational simulation using density functional theory (DFT) has also been conducted to supplement the experimental Raman analyses for crystalline Si and SiO₂. XPS results reveal that ca. 30 % of the SiNWs have been oxidized for all substrates. The results presented in this paper can be used to aid selection of appropriate substrates for SiNW growth, depending on specific applications.     

从不可能中学习

经典基础物理学建构在已经发生的事实基础之上,具有简洁而优美的表述,因而让很多人都相信宇宙的确可能存在这样的拉普拉斯“兽”,它可以通过精确的初始条件和完备的物理定律而洞悉过去和将来的一切。这一“世界决定论”,将世间发生的一切视为“上天注定”,更让许多人相信万物归于本源、复杂启于简单的“还原论”。持有这些观点的人们通常认为从来没有发生过的事情一定是不可能的,而反设事实(counterfactual)允许我们对已经发生的事实进行否定推设,继而构建基于可能性的逻辑推理。显然,经典物理并不包括假设性或反设事实的事件。     

Complex Geometry and Dirac Equation

Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit . We discuss two possibilities which appearin the multivector algebra approach: the₁₂₃ and ₂₁ complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit is also discussed.     

Infrared Spectra of the Square Planar Rhodium(I) Complexes cis-[Rh(CO)2(pyridine) (X)] (X = Cl,Br): Isotopic Labelling Studies and Normal Coordinate Analysis

Abstract

The infrared spectra (4000 - 50 cm^?1) of the square planar rhodium(I) complexes cis-[Rh(CO)₂ (pyridine) (X)] (X = Cl, Br) and their isotopomers with pyridine-d ₅ and ¹³CO have been determined. Assignments are based on earlier studies on pyridine and its complexes and on the shifts in infrared bands which are caused by the isotopic substitutions employed. Normal coordinate analysis following the procedure of Becher and Mattes has been used to confirm the empirical assignments. The two v(RhC) bands are observed near 490 and 450 cm^?1. v(RhN) is found near 210 cm^?1 and v(RhX) occurs at 310 (X = Cl) and 235 (X = Br) cm^?1. At frequencies below 200 cm^?1, the bands are assigned to bending modes in the following sequence: δ (RhN) > δ (CRhC) > δ (RhCl) > γ (RhCl) > γ (RhN).