Unstable Semiclassical Trajectories in Tunneling

Some tunneling phenomena are described, in the semiclassical approximation, by unstable complex trajectories. We develop a systematic procedure to stabilize the trajectories and to calculate the tunneling probability, including both the suppression exponent and prefactor. We find that the instability of tunneling solutions modifies the power-law dependence of the prefactor on h as compared to the case of stable solutions.Comment: Journal version; 4 pages, 2 figure

Automatic selection of a subset size at vector fields construction

An algorithm for selection of the size of a correlation kernel at displacement vector field construction by the method of digital image correlation has been proposed. The algorithm has been tested on simulated and experimental optical images having different texture. The influence of the correlation kernel size and image texture on nose immunity at determining displacements has been studied. It is shown that the proposed algorithm allows to find this size providing the minimum error when determination of displacements and estimation of deformation

Overbarrier reflection in quantum mechanics with multiple degrees of freedom

We present an analytic example of two dimensional quantum mechanical system, where the exponential suppression of the probability of over-barrier reflection changes non-monotonically with energy. The suppression is minimal at certain "optimal" energies where reflection occurs with exponentially larger probability than at other energies

Complex trajectories in chaotic dynamical tunneling

We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the classical ones. This provides a natural classification of the tunneling solutions. Second, we present a heuristic procedure for sorting out the least suppressed trajectory. As an illustration, we apply our technique to the process of chaotic tunneling in a quantum mechanical model with two degrees of freedom. Our analysis reveals rich dynamics of the system. At the classical level, there exists an infinite set of unstable solutions forming a fractal structure. This structure is inherited by the complex tunneling paths and plays the central role in the semiclassical study. The process we consider exhibits the phenomenon of optimal tunneling: the suppression exponent of the tunneling probability has a local minimum at a certain energy which is thus (locally) the optimal energy for tunneling. We test the proposed method by comparison of the semiclassical results with the results of the exact quantum computations and find a good agreement

A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

Brittle or Quasi-Brittle Fracture of Engineering Materials: Recent Developments and New Challenges

1 Department of Management and Engineering, University of Padova, Stradella San Nicola 3, 36100 Vicenza, Italy 2 Departamento de Ciencia de Materiales, Universidad Politecnica de Madrid, E. T. S. de Ingenieros de Caminos Canales y Puertos C/ Profesor Aranguren s/n, 28040 Madrid, Spain 3 Fatigue and Fracture Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran 4Department of Mechanical Engineering & Aeronautics, Institute of Strength Physics and Material Science, Siberian Branch of Russian Academy of Sciences, Tomsk 634021, Russia 5 Laboratory of Technology & Strength of Materials (LTSM), Department of Mechanical Engineering & Aeronautics, University of Patras, 26500 Patras, Greec

Influence of ion-beam treatment on structure and defor-mation resistance of 12Cr1MoV steel under static, cyclic and dynamic loading

Features of modification of structure and properties of 12Cr1MoV steel subjected to ion-beam irradiation by zirconium ion beam have been investigated with the use of optical and electron microscopy, and microhardness measurement. It was shown that after the treat-ment the modification occurs across the entire cross-section of specimens with the thickness of 1 mm. Changes in mechanical properties of these specimens under static, cyclic and impact loading were interpreted in terms of identified structure modifications

Investigation of the effect of combined thermomechanical processing on the brass microstructure evolution and the microhardness change

The article investigates the effect of combined thermomechanical processing, including pre-heat treatment and radial-shear rolling on the brass microstructure evolution and the microhardness change. The microstructure analysis of heat-treated samples according to various modes showed that the most optimal heat treatment before radialshear rolling for L63 brass is annealing at a temperature of 500 °C. As a result of combined thermomechanical processing, a gradient structure was obtained, so in the resulting rods with a diameter of 16 mm in the surface layer, a structure with an average grain size of 9 μm was obtained. In rods with a diameter of 12 mm, a fine–grained, equalgrained structure of 3 μm was obtained in the surface layer

Signatures of unstable semiclassical trajectories in tunneling

It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we find an additional power-law dependence of the tunneling probability on the semiclassical parameter as compared to the standard case of potential tunneling. The second signature is substantial widening of the probability distribution over final-state quantum numbers. These effects are studied using modified semiclassical technique which incorporates stabilization of the tunneling trajectories. The technique is derived from first principles. We obtain expressions for the inclusive and exclusive tunneling probabilities in the case of unstable semiclassical trajectories. We also investigate the "phase transition" between the cases of stable and unstable trajectories across certain "critical" value of energy. Finally, we derive the relation between the semiclassical probabilities of tunneling from the low-lying and highly excited initial states. This puts on firm ground a conjecture made previously in the semiclassical description of collision-induced tunneling in field theory.Comment: Journal version; 48 pages, 16 figure

Investigation of the effect of combined thermomechanical processing on the brass microstructure evolution and the microhardness change

The article investigates the effect of combined thermomechanical processing, including pre-heat treatment and radial-shear rolling on the brass microstructure evolution and the microhardness change. The microstructure analysis of heat-treated samples according to various modes showed that the most optimal heat treatment before radialshear rolling for L63 brass is annealing at a temperature of 500 °C. As a result of combined thermomechanical processing, a gradient structure was obtained, so in the resulting rods with a diameter of 16 mm in the surface layer, a structure with an average grain size of 9 μm was obtained. In rods with a diameter of 12 mm, a fine–grained, equalgrained structure of 3 μm was obtained in the surface layer