Anomalous Magneto-Oscillations

The principal families of periodic orbits that emerge from the stationary points of the six-dimensional potential energy surface of the C2H2 molecular system, as well as periodic orbits from saddle-node bifurcations, have been located and propagated for an energy range up to 36 500 cm−1 above the absolute minimum of the potential. The bifurcation diagrams of these periodic orbits reveal the regions of phase space where the dynamics are regular or chaotic (with soft or hard chaos) for acetylene, vinylidene, and the region over these two isomers. An association of the structure of phase space with spectroscopic findings is made by calculating Gutzwiller’s semiclassical trace formula and classical survival probability functions.

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Using quantum maps, we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy in some systems is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues.

We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate‐space formulation. Using a coherent‐state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum‐mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.

This chapter is dedicated to the derivation of semiclassical trace formulae for particles with spin. We will focus on Pauli Hamiltonians with arbitrary spin and only briefly describe the corresponding calculations for the Dirac equation. We will also comment on a different limit in which the spectral asymptotics of the Pauli Hamiltonian can be considered.KeywordsPeriodic OrbitDirac EquationJacobi EquationTrace FormulaOrbit CouplingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We investigate quantized maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i.e. it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantization without altering the classical limit of the dynamics on the torus, we numerically observe a transition to RMT statistics. The results are interpreted in terms of semiclassical trace formulae for the maps with and without spin, respectively. We thus have constructed quantum systems with non-mixing classical limit which show generic (i.e. RMT) spectral statistics. We also discuss the analogous situation for an almost-integrable map, where we compare to semi-Poissonian statistics.

The electronic supershell structure of simple metal clusters in a uniform magnetic field is studied with a spherical infinite-well potential as a simple yet realistic model for confining the valence electrons. It is found that there is little perceivable change in the supershells with experimentally achievable field strengths. If yet stronger fields are applied, the supershell structure gets destroyed and then new beat structures come about as the field strength increases further. These phenomena are explained by a recently derived semiclassical trace formula for broken symmetry that has been applied to the present system. \textcopyright{} 1996 The American Physical Society.

We consider the effect of a continuous family of neutral (bouncing ball) orbits on the energy spectrum of the quantized stadium billiard. Using a semiclassical approximation we derive analytic expressions for standard two-point spectral measures. The corrections due to the bouncing ball orbits account for some of the non-generic features observed in the analysis of the spectrum of a stadium cavity which was recently measured. Once the bouncing ball contributions are subtracted, the spectrum is shown to be well reproduced by the semi-classical trace formula based on unstable periodic orbits. We also study special patterns in the spectrum which are due to other non-generic features such as edge effects and 'whispering gallery' trajectories.

A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace formula for star graphs, and on diagrammatic techniques. The appropriate spectral form factors are calculated up to one order beyond the diagonal and self-dual approximations. The results are in accordance with the corresponding random-matrix theories which supports a properly generalized Bohigas-Giannoni-Schmit conjecture.

The effect of progressive damages in composite materials is incorporated into a geometrically nonlinear solid shell element formulation to investigate the dynamic response of composite structures under the blast wave pressure loading. The effect of material damages such as fiber failures, matrix cracking, and fiber-matrix shearing failures on the behavior of composite structures is addressed via reducing their stiffness corresponding to detected failures. Two separate failure criteria are used for unidirectional and woven composites. In addition, the strain-rate effect on the material strength is taken into account. For the dynamic formulation, the trapezoidal rule is chosen for the time integration. Various numerical analyses of composite panels are conducted under the static and dynamic loading conditions to validate the effectiveness of the present formulation. The analysis results clearly exhibit the significant effect of material damages on the structural behavior of the composite panels. Also, the analysis results are in good agreement with the available experimental data.

본 연구에서는 수중 음향 트랜스듀서의 주파수 광대역화를 위해서 중공형 전면추를 가진 Tonpilz 트랜스듀서를 제안하였다. 트랜스듀서의 특성에 미치는 설계변수들의 영향을 분석하고, 그 결과에 따라 Tonpilz 트랜스듀서의 최적구조를 설계하였다. 나아가 시편의 제작 및 특성 측정을 통하여 설계 결과의 타당성을 검증하였다. 설계된 트랜스듀서는 단일모드 트랜스듀서에 비해 월등히 넓은 131 %의 -6 dB 비대역폭을 나타내었으며, 해석 결과와 측정 결과가 잘 일치하는 것으로 확인되었다. In this work, we present an underwater acoustic transducer with a cavity-type head mass to achieve a wide frequency bandwidth. We analyzed the effects of design variables on the transducer characteristics, and optimized the structure of the Tonpilz transducer based on the analysis results. Further, validity of the design was verified by manufacturing a prototype of the transducer and measuring its properties. The designed transducer had a far wider -6 dB fractional bandwidth which is 131 % than that of a single mode transducer, and the measured results were confirmed to be in good agreement with the analysis results.

The aim of this work was to study the feasibility and reproducibility of in vivo measurement of benzodiazepine receptors with single photon emission computerized tomography (SPECT) in the baboon brain. Arterial and brain regional activities were measured for 420 min in three baboons after single bolus injection of the benzodiazepine antagonist [123I]iomazenil. Data were fit to a three-compartment model to derive the regional binding potential (BP), which corresponds to the product of the receptor density, (Bmax) and affinity (1/KD). Regional BP values (from 114 in striatum to 241 in occipital) were in good agreement with values predicted from in vitro studies. Constraining the regional volume of distribution of the nondisplaceable compartment to the value measured during tracer constant infusion experiments in baboons (Laruelle et al., 1993) improved the identifiability of the rate constants. Each experiment was repeated to investigate the reproducibility of the measurement. The regional average reproducibility was 10 +/- 5%, expressed as coefficient of variation (CV). Results of equilibrium analysis at peak uptake were in good agreement with results of kinetic analysis. Empirical counts ratio methods were found to be poorly sensitive to benzodiazepine receptor density. These studies suggest the feasibility of quantitative measurement of benzodiazepine receptors by kinetic analysis of SPECT data and the inadequacy of empirical methods of analysis, such as counts ratios, to evaluate differences in receptor density.

We show that we are able to extract the pion electromagnetic form factor by using the recent charged pion electroproduction data from JLab and a simple t-channel diagram. For this purpose we have performed the Q2-independent and dependent analyses. The result of the first analysis is in good agreement with those of previous works and fit the Maris and Tandy model as well as the monopole parametrization which describes a pion radius of 0.672 fm. The result of the second analysis corroborates the findings in the first analysis. Our findings therefore provide a direct proof that at the given kinematics the t-channel diagram really dominates the process. This could also set a new constraint to the phenomenological models that try to describe the process.

In present paper the Equal Channel Angular Extrusion (ECAE) through a rectangular die was firstly physically simulated using plasticine and then theoretically analyzed by upper bound method. Physical simulation was used to identify the deformation zone and as a background for the following theoretical ECAE analysis by rigid block model. The plane strain deformation mode and ideal plasticity of an extruded material were assumed. The dependencies of ECAE pressure, accumulated shear and dimension of a "dead zone" upon friction factor were analytically determined. The rise in ECAE pressure, accumulated shear and size of a "dead zone" with the increase in friction was predicted. The obtained results were compared with the slip line based solution and a good agreement between them was found. Finally the results of upper bound analysis were discussed together with the results of experimental investigations and finite element analysis of ECAE mechanics published elsewhere.

The mechanics of equal channel angular extrusion (ECAE) in a rectangular die was studied by upper bound method and rigid block model of deformation with two variables (two degrees of freedom). The appearance of a dead zone in the die external corner was assumed and verified by physical simulation using plasticine as a modeling material. The obtained dependences of ECAE pressure, total ECAE shear and geometrical parameters of dead zone upon friction factor were compared with corresponding results of upper bound rigid block analysis with one variable (one degree of freedom) and with the results of slip line analysis published by the authors elsewhere. It was demonstrated that an increase in degrees of freedom in an ECAE rigid block model from one to two results in much better approximation of the reference data of slip line analysis. The authors believe that an increase in the numbers of degrees of freedom and flexibility of a rigid block model generally leads to a better accuracy in modeling of other metal forming processes as well. As an example, the ECAE pressure of the aluminum 6061 alloy was calculated and compared with the experimental data from literature. A good agreement between them was found. The importance of consideration of friction in the inlet and outlet die channels was emphasized.