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

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

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

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

Multi-purpose fatigue sensor

Frattura ed Integrità Strutturale, Issue 38 (2016);The paper describes the key principles and results of preliminary experiments aimed at the development of new technique for the fatigue life prediction under conditions of biaxial cyclic tension. The foundations of the method were developed early by the numerous tests with monitoring the process of surface deformation relief formation, which is proved to be an indicator of accumulated fatigue damage under uniaxial fatigue. The employed phenomenon was early applied for the development of a family of uniaxial loading fatigue sensors. The formation of strain induced relief has been recently taken into consideration as a part of damage accumulation criteria under biaxial fatigue as well. The home-made testing machine has been designed to implement combined bending and torsion loading that simulates loads experienced by an aircraft wing skin. The experimental evidences on formation and evolution of the deformation relief revealed under conditions of combined loading, supports the proposed concept of biaxial fatigue sensor. The characteristic informative parameters for defect detection to be used in fatigue sensors have been established. Their development is interpreted in terms of scale levels of deformation and fracture. Damage accumulation of the sensor’s surface tends to exhibit the self-organization nature. It is accompanied by formation of "folded" strain-induced relief on the surface. The mechanisms of damage accumulation under cyclic deformation were analyzed with the use of the multiscale approach

analysis and automated fatigue damage evaluation of a 17mn1si pipeline steel

Abstract Digital identification and evaluation of the fatigue damage accumulation kinetics on the surface of the fatigue sensor from steel 17Mn1Si is performed using the digital image processing method. The accumulation of defects was assessed based on the analysis of the diagnostic results for individual stages of cyclic deformation. It is established that the graded nature of the fatigue crack growth is in a good agreement with the parameters of the image of the analyzed surface. Based on the gradual processing of the results obtained for the surface damage the main regularities in the development of shear and rotational processes are found. The theoretical preconditions and experimental results are presented

Molecular dynamics study of cluster structure and properties of rotational waves in solid nanostructures

The paper reports a molecular dynamics analysis of rotary properties of a transformational wave generated due to compressive influence. Studies are performed in the time interval prior to the onset of elastic precursor reflection from the free boundary. It is shown that the leading front of a rotary wave coincides with the transformational wave front. The rotary wave velocity for copper is determined, being equal to 1300 m/s. The values of angular moment projections onto the coordinate axes in a plane perpendicular to wave propagation are found to be symmetrical, and their total sum equals zero

Molecular dynamics study of cluster structure and properties of rotational waves in solid nanostructures

The paper reports a molecular dynamics analysis of rotary properties of a transformational wave generated due to compressive influence. Studies are performed in the time interval prior to the onset of elastic precursor reflection from the free boundary. It is shown that the leading front of a rotary wave coincides with the transformational wave front. The rotary wave velocity for copper is determined, being equal to 1300 m/s. The values of angular moment projections onto the coordinate axes in a plane perpendicular to wave propagation are found to be symmetrical, and their total sum equals zero

Increasing Fatigue LIfe of 09Mn2Si Steel by means of High-Temperature Multistep Helical Rolling

The effect of high temperature helical rolling (HR) on structure and fatigue life of 09Mn2Si pipe steel has been studied. With the use of transmission electron microscopy there was revealed that rolling gives rise to refinement of ferrite grains and cracking (fracturing) of cementite plates within the pearlite phase. The effect manifests itself to the greatest extent in the surface layer where due to the rolling the level of plastic deformation was the highest. Data of microhardness measurements confirms the gradient pattern of strain hardening over the cross section during the HR occurs while the most intensive microhardness increasing take place at the depth of up to 3 mm. According to the mechanical testing results the helical rolling of 09Mn2Si steel gives rise to increasing the level of deforming stress at the yield plateau as well as the proportionality limit with a general decrease in the relative elongation. At the same time, despite the strain hardening resulting from the helical rolling the mechanisms of plastic deformation which manifest themselves in the form of parabolic hardening with a smooth decrease in the flow stress level after neck formation are preserved in the steel. During the cyclic tension the number of cycles prior to failure increases from 2.5 to 3.8 times that depends on the location of specimens' cutting from the rolled rod. The highest improvement in fatigue fracture resistance is registered for specimens cut out from the core of the rolled rods

Increasing Fatigue LIfe of 09Mn2Si Steel by means of High-Temperature Multistep Helical Rolling

The effect of high temperature helical rolling (HR) on structure and fatigue life of 09Mn2Si pipe steel has been studied. With the use of transmission electron microscopy there was revealed that rolling gives rise to refinement of ferrite grains and cracking (fracturing) of cementite plates within the pearlite phase. The effect manifests itself to the greatest extent in the surface layer where due to the rolling the level of plastic deformation was the highest. Data of microhardness measurements confirms the gradient pattern of strain hardening over the cross section during the HR occurs while the most intensive microhardness increasing take place at the depth of up to 3 mm. According to the mechanical testing results the helical rolling of 09Mn2Si steel gives rise to increasing the level of deforming stress at the yield plateau as well as the proportionality limit with a general decrease in the relative elongation. At the same time, despite the strain hardening resulting from the helical rolling the mechanisms of plastic deformation which manifest themselves in the form of parabolic hardening with a smooth decrease in the flow stress level after neck formation are preserved in the steel. During the cyclic tension the number of cycles prior to failure increases from 2.5 to 3.8 times that depends on the location of specimens' cutting from the rolled rod. The highest improvement in fatigue fracture resistance is registered for specimens cut out from the core of the rolled rods