Swinging Atwood Machine: Experimental and numerical results, and a theoretical study

A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have non-negligible radii and masses. Equations of motion must therefore take into account the moment of inertia of the pulleys, as well as the winding of the rope around them. Their influence is compared to previous studies. A preliminary discussion of the role of dissipation is included. The theoretical behaviour of the system with pulleys is illustrated numerically, and the relevance of different parameters is highlighted. Finally, the integrability of the dynamic system is studied, the main result being that the machine with pulleys is non-integrable. The status of the results on integrability of the pulley-less machine is also recalled.     

Physical and numerical verification of discharge calculations

Calculations of radio frequency discharge parameters, and to a lesser extent DC discharge parameters, are apparently highly sensitive to the physical model used. The testing of numerical schemes for error, considering alternative formulations and simple physical models, is carefully considered. Within kinetic models a number of options exist, having different capabilities, the implications of which are examined. Particle simulations are discussed, and mesh-based kinetic calculations are considered in detail. An efficient and accurate mesh-based kinetic model which closely replicates the physical processes taking place is presented. Ways to improve its accuracy, which is limited by the resolution of the mesh, and their effects are presented. Cross-checking of various numerical formulations shows that the results for each are essentially the same. Physical reasoning and simple estimates of discharge parameters are used to further substantiate the predictions for a particular discharge, and the processes taking place in an RF discharge in helium are described in detail     

Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results

A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.     

Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations

In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.     

Tweed microstructures: Experimental observations and some theoretical models

Experimental observations, mainly by transmission electron microscopy, of tweed microstructures in minerals (K-feldspar and cordierite), high-T _c superconductors (Co-doped YBCO) and metals are reviewed. Structural models of the local structure within the tweed are compared and evaluated with respect to spectroscopic measurements in a number of systems. It is concluded that in tweed microstructures which result from symmetry changes driven by cation-ordering, the local degree of order is not itself modulated. A model based on twin-related domains of the low symmetry form is consistent with experimental observations. Mechanisms of coarsening of the tweed microstructure to form the lamellar twinning observed in the fully ordered structure are briefly reviewed.     

Experimental and theoretical Raman results in trans polyacetylene

We present here the experimental and theoretical calculations of Resonant Raman scattering from trans (CH)_x. The new experimental data obtained with U.V. exciting wavelengths are interpreted in terms of the theoretical model based on the bimodal statistical distribution of long and short chains which constitute a given trans (CH)_x sample.     

Lifetimes and transition probabilities of Xe II: Experimental measurements and theoretical calculations

In this work we make an experimental and theoretical investigation of transition probabilities (A) and lifetimes of Xe II. Eighteen A_ij's corresponding to the 6p-6d array were measured using a Laser Produced Plasma (LPP) as the spectroscopic source. The ab initio (AI) and Least Square Fitting (LSF) approaches were used to calculate the atomic parameters. Relativistic corrections and Configuration Interaction (CI) effects have been taken into account using the HFR approach described by Cowan. Whereas the AI parameters corresponding to 6p levels are not very affected by CI effects, several of the 6d levels with J=1/2, 3/2and 5/2 making transitions to the fundamental levels 5p⁵ are affected by CI effects due to both, discrete nd and continuum states, modifying their lifetimes values. An extensive comparison with other measurements and calculations are made. In particular, concerned with branching ratio and forbidden transitions. Received 15 July 1999     

Some theoretical and numerical results for delayed neural field equations

In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integro-differential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential equations, we show the existence and uniqueness of a solution of these equations. A Lyapunov analysis gives us sufficient conditions for the solutions to be asymptotically stable. We also present a fairly detailed study of the numerical computation of these solutions. This is, to our knowledge, the first time that a serious analysis of the problem of the existence and uniqueness of a solution of these equations has been performed. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our numerical schemes on a variety of examples that are relevant to modeling in neuroscience.     

Experimental measurement and theoretical analyses of the freezing-thawing processes around a probe

Both the experimental and the analytical studies of the freezing/thawing process around a cryosurgical cylinder probes in a simulative biological tissue are presented in this paper. The enthalpy method and the finite element scheme are applied to solve the multidimensional phase change problems in cryosurgery. A very good agreement is found between the computed solutions and the experimental results. The influences of different cooling-warming schemes of the probe on the ice ball development, the temperature variation, the axial and the radial temperature gradients inside the tissues, and the requirement of cooling power are analyzed     

受激散射过程理论模型的发展与应用

在激光间接驱动的惯性约束聚变（ICF）中,高强度激光与低密度等离子体发生相互作用,会激发两种受激散射过程：受激布里渊散射和受激拉曼散射。它们会损失激光能量、破坏辐射场对称性、产生超热电子,从而危害聚变点火过程。因此,理解受激散射的物理过程并找到抑制其发展的有效方法,是ICF研究中重点关注的问题。介绍了中国激光聚变研究团队为研究受激散射过程而发展的多个理论模型,以及这些模型在实验数据分析中的具体应用。这些理论模型与实验研究一起,为提升受激散射过程的物理理解发挥了重要作用。     

Nuclear quadrupole interaction in metals: Experiments, calculations, models

The results obtained from the investigation of the nuclear quadrupole interaction in metals, mostly at impurities, are reviewed. Examples of the experimental work are primarily taken from studies at ISOLDE/CERN. For the determination of the nuclear quadrupole moments Q, necessary to extract the electric field gradients from the measured coupling constants, various methods have been employed. Band structure calculations both for pure systems and also for impurities have been performed with the FLAPW density functional method. The theoretical understanding achieved for sp-impurities in simple noncubic metals is described. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal isomerization and cyclization of 1-naphthylacetylene: Experimental results, quantum chemical and transition state theory calculations

The isomerization of 1-naphthylacetylene diluted in argon was studied behind reflected shock waves in a 2 in i.d. single pulse shock tube over the temperature range 1000-1250 K and overall densities of ∼3 × 10⁻⁵ mol/cm³. The only reaction product found in the post shock mixtures was acenaphthylene. The first order rate constant of the isomerization was found to be k = 2.08 × 10¹² exp(−54.2 × 10³/RT) s⁻¹, where R is expressed in units of cal/K mol. Potential energy surfaces of the cyclization reaction 1-naphthylacetylene → acenaphthylene and the isomerization 1-naphthylacetylene → 2-naphthylacetylene were calculated using the Becke three-parameter hybrid method with Lee-Yang-Parr correlation functional approximation (B3LYP). Structure, energy and frequency calculations were carried out with the Dunning correlation consistent polarized double ζ (cc-pVDZ) basis set. The rate constant (k_∞) for the 1-naphthylacetylene → acenaphthylene cyclization was calculated using transition state theory, the value obtained is k_∞ = 3.52 × 10¹² exp(−55.9 × 10³/RT) s⁻¹, where R is expressed in units of cal/K mol. The agreement between the experiment and the calculations is very good. RRKM calculations were done to transfer k_∞ to the pressure of the single pulse shock tube experiments. In view of high temperature and the large molecule involved the deviation from k_∞ is very small. The isomerization 1-naphthylacetylene → 2-naphthylacetylene proceeds via the formation of an unstable intermediate 1,2-naphthalenocyclobutene and has a high barrier of ∼83.5 kcal/mol. In view of this high barrier, the isomerization cannot compete with the cyclization that proceeds with a barrier of ∼56 kcal/mol.     

Comparison of WKB calculations and experimental results for three-dimensional cochlear models.

The WKB asymptotic method is applied to the calculation of cochlear models with square scala cross section, for which the fluid motion is fully three dimensional. The analysis begins with the exact solution for wave propagation in a duct with constant properties. This solution is somewhat tedious but straightforward, since it requires a Fourier series expansion across the duct. Then with the formulation of Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)], the approximate solution is readily generated for the duct with properties which vary slowly along the length. Numerical calculations are carried out for the experimental models of Cannel [Ph.D. thesis, Univ. of Warwick (1969)] and Helle [Dr.-Ing. disser., Technische Univ., Müchen (1974)] who furnish quantitative details of both "basilar membrane" response and model parameters. Without any free parameters for adjusting, the present WKB solution shows quite satisfactory agreement with the experimental model results. Computer time is reasonable; the calculation of displacement envelope and phase at a number of stations along the cochlea for a given frequency requires only one second of CPU time. Thus the credibility and practically of the approach is established for the investigation of yet more realistic and more elaborate cochlear models.