Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Fully Comprehensive Geometrically Non-Linear Dynamic Analysis of Multi-Body Beam Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of flexible,non-linear multi-body beam systems. The focus is on problems where the strains within each elastic body (beam) remain small. Based on geometrically non-linear elasticity theory, the non-linear 3-D beam problem splits into either a linear or non-linear 2-D analysis of the beam cross-section and a non-linear 1-D analysis along the beam reference line. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction,results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis,the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.The analysis methodology can be viewed as a 3-step procedure. First, the sectional properties of beams made of composite materials are determined either based on an asymptotic procedure that involves a 2-D finite element nonlinear analysis of the beam cross-section to capture trapeze effect or using strip-like beam analysis, starting from Classical Laminated Shell Theory (CLST). Second, the dynamic response of non-linear, flexible multi-body beam systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for non-linear beam systems. Finally,local 3-D responses in the beams are recovered, based on the 1-D responses predicted in the second step. Numerical examples are presented and results from this analysis are compared with those available in the literature.

Codes for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces

Three codes, that can solve three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces, are provided here. The file 'bemconst.m' contains a MATLAB code for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces. The file 'bemconst.f90' is a Fortran translation of the MATLAB code contained in the file 'bemconst.m'. The file 'bemconstp.f90' is a parallelized version of the Fortran code contained in the file 'bemconst.f90'. The file 'inbem96.txt' is the input file for the Fortran codes contained in the files 'bemconst.f90' and 'bemconstp.f90'. Author hereby declares that the present codes are the original works of the author. Further, author hereby declares that any of the present codes, in full or in part, is not a translation or a copy of any of the existing codes written by someone else. Author's institution (Indian Institute of Science) has informed the author in writing that the institution is not interested in claiming any copyright on the present codes. Author is hereby distributing the present codes under the MIT License; full text of the license is included in each of the files that contain the codes.

Studies on the wobble mode stability of a three-wheeled vehicle

A wobble instability is one of the major problems of a three-wheeled vehicle commonly used in India, and these instabilities are of great interest to industry and academia. In this paper, we studied this instability using a multi-body dynamic model and with experiments conducted on a prototype three-wheeled vehicle on a test track. The multi-body dynamic model of a three-wheeled vehicle is developed using the commercial software ADAMS/Car. In an initial model, all components including main structures such as the frame, the steering column and the rear forks are assumed to be rigid bodies. A linear eigenvalue analysis, which is carried out at different speeds, reveals a mode that has predominantly a steering oscillation, also called a wobble mode, with a frequency of around 5-6Hz. The analysis results shows that the damping of this mode is low but positive up to the maximum speed of the three-wheeled vehicle. However, the experimental study shows that the mode is unstable at speeds below 8.33m/s. To predict and study this instability in detail, a more refined model of the three-wheeled vehicle, with flexibilities of three important bodies, was constructed in ADAMS/Car. With flexible bodies, three modes of a steering oscillation were observed. Two of these are well damped and the other is lightly damped with negative damping at lower speeds. Simulation results with flexibility incorporated show a good match with the instability observed in the experimental studies. Further, we investigated the effect of each flexible body and found that the flexibility of the steering column is the major contributor for wobble instability and is similar to the wheel shimmy problem in aircraft.

Three-dimensional warping in strip-based composite four-bar mechanisms

This work intends to demonstrate the effect of geometrically non-linear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting the three-dimensional warping of the cross-section. The only restriction in the present analysis is that the strains within each elastic body remain small (i.e., this work does not deal with materials exhibiting non-linear constitutive laws at the 3-D level). Here, all component bars of the mechanism are made of fiber-reinforced laminates. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction, results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis, the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here. The representative cross-sections of all component bars are analyzed using two different approaches: (1) Numerical Model and (2) Analytical Model. Four-bar mechanisms are analyzed using the above two approaches for Omega = 20 rad/s and Omega = pi rad/s and observed the same behavior in both cases. The noticeable snap-shots of the deformation shapes of the mechanism about 1000 frames are also reported using commercial software (I-DEAS + NASTRAN + ADAMS). The maximum out-of-plane warping of the cross-section is observed at the mid-span of bar-1, bar-2 and bar-3 are 1.5 mm, 250 mm and 1.0 mm, respectively, for t = 0:5 s. (C) 2015 Elsevier Ltd. All rights reserved.

Justifying threshold voltage definition for undoped body transistors through ``crossover point'' concept

Two different definitions, one is potential based and the other is charge based, are used in the literatures to define the threshold voltage of undoped body symmetric double gate transistors. This paper, by introducing a novel concept of crossover point, proves that the charge based definition is more accurate than the potential based definition. It is shown that for a given channel length the potential based definition predicts anomalous change in threshold voltage with body thickness variation while the charge based definition results in monotonous change. The threshold voltage is then extracted from drain current versus gate voltage characteristics using linear extrapolation, transconductance and match-point methods. In all the three cases it is found that trend of threshold voltage variation support the charge based definition.

The three faces of Maxwell�s equations

In dealing with electromagnetic phenomena and in particular the phenomena of optics, despite the recognition of the quanta of light people tend to talk of the amplitudes and field strengths, as if the electromagnetic field were a classical field. For example we measure the wavelength of light by studying interference fringes. In this paper we study the inter-relationship of three ways of looking at the problem: in terms of classical wave fields, wave function of the photon; and the quantized wave field. The comparison and contrasts of these three modes of description are carefully analyzed in this paper. The ways in which these different modes complement our intuition and insight are also discussed.

Unsteady free Convection MHD Boundary Layer Flow Near a Three-Dimensional Stagnation Point

The unsteady free convection boundary layer hydromagnectic flow near a stagnation point of a three-dimensional body with applied magnetic field and time-dependent wall temperature has been studied. Both semi-semilar and self-similar cases have been considered. The equations governing the above flow have been solved numerically using an implicit finite-difference scheme due to Keller. The magnetic field is found to reduce both the heat transfer and skin friction. The effect of the variation of the wall temperature with time and of mass transfer is found to be more pronounced on the heat transfer than on the skin friction. In self-similar case, for decelerating flow, there is temperature overshoot in the presence of fmagnetic field, but in semi-similar case overshoot occurs even without magnetic field due to the unsteadiness

Unsteady laminar incompressible second-order boundary-layer flow at a three-dimensional stagnation point

The unsteadely laminar incompressible second-order boundary-layer flow at the stagnation point of a three-dimensional body has been studied for both nodal and saddle point regions. The effects of mass transfer and Prandtl number have been taken into account. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It has been found that the parameter characterizing the unsteadiness in the velocity of the free stream, the nature of the stagnation point, the mass transfer and Prandtl number strongly affect the second-order skin friction and heat transfer. The overall skin friction becomes less due to second-order effects but the heat transfer has the opposite behaviour. For large injection, the second-order skin-friction and heat-transfer results prevail over the first-order boundary layer results whereas for the case of large suction the behaviour is just the opposite.

Three-dimensional elastic analysis of cracked thick plates under bending fields

A three-dimensional analysis is presented for the bending problem of finite thick plates with through-the-thickness cracks. A general solution is obtained for Navier's equations of the theory of elasticity. It is found that the in-plane stresses and the transverse normal stress at the crack front are singular with an inverse square root singularity, while the transverse shear stresses are of the order of unity. Results from a numerical study indicate that the stress intensity factor, which varies across the thickness, is influenced by the thickness ratio in a significant manner. Results from a parametric study and those from a comparative study with existing finite element values are presented.

Quasi-2D XY Magnetic Properties and Slow Relaxation in a Body Centered Metal Organic Network of [Co-4] Clusters

Octahedral Co2+ centers have been connected by mu(3)-OH and mu(2)-OH2 units forming [Co-4] clusters which are linked by pyrazine forming a two-dimensional network. The two-dimensional layers are bridged by oxybisbenzoate (OBA) ligands giving rise to a three-dimensional structure. The [Co-4] clusters bond with the pyrazine and the OBA results in a body-centered arrangement of the clusters, which has been observed for the first time. Magnetic studies reveal a noncollinear frustrated spin structure of the bitriangular cluster, resulting in a net magnetic moment of 1.4 mu B per cluster. For T > 32 K, the correlation length of the cluster moments shows a stretched-exponential temperature dependence typical of a Berezinskii-Kosterlitz-Thouless model, which points to a quasi-2D XY behavior. At lower temperature and down to 14 K, the compound behaves as a soft ferromagnet and a slow relaxation is observed, with an energy barrier of ca. 500 K. Then, on further cooling, a hysteretic behavior takes place with a coercive field that reaches 5 Tat 4 K. The slow relaxation is assigned to the creation/annihilation of vortex-antivortex pairs, which are the elementary excitations of a 2D XY spin system.

Two-Impurity Kondo Problem

The two-impurity Kondo problem is studied by use of perturbative scaling techniques. The physics is determined by the interplay between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins and the Kondo effect. In particular, for a strong ferromagnetic RKKY interaction the susceptibility exhibits three structures as the temperature is lowered, corresponding to the ferromagnetic locking together of the two impurity spins followed by a two-stage freezing out of their local moments by the conduction electrons due to the Kondo effect.

Determination of the optically equivalent model in three-dimensional photoelasticity

Any stressed photoelastic medium can be reduced to an optically equivalent model consisting of a linear retarder, with retardation 1 and principal axis at azimuth 1, and a pure rotator of power 2. The paper describes two simple methods to determine these quantities experimentally. Further, a method is described to overcome the problem of rotational effects in scattered-light investigations. This new method makes use of the experimentally determined characteristic parameters