Measurement of proper time in a Weyl space

In a Weyl space it is possible to construct geometrical clocks along timelike geodesics using projective and conformal techniques. We present a precise definition of the limiting processes involved and prove analytically that the clock readings coincide with an affine parameter of the Weyl connection.     

Maximal proper acceleration and the structure of spacetime

A limiting proper acceleration in nature follows deductively from known physics and compels the union of spacetime and four-velocity space into a maximal-acceleration invariant phase space having an intrinsic Kaluza-Klein-type fiber-bundle structure with manifest gauge properties. The Riemann curvature scalar of the bundle manifold is determined, and a possible action principle is considered to serve as a basis for the generation of field equations.1. This is an expanded version of an invited paper presented at the Fifth Marcel Grossmann Meeting at the University of Western Australia, 8–12 August 1988.     

Hyperspin manifolds and the space problem of Weyl

A recent criticism of the claimed existence of torsion-free connections compatible with a hypermanifold structure in Finkelstein's sense is reinforced by relating the problem to the space problem of Weyl as generalized by Cartan and Freudenthal. Some historical remarks concerning the development of the latter are also included.     

Magneto-transport properties of thin flakes of Weyl semiconductor tellurium

As an elemental semiconductor, tellurium has recently attracted intense interest due to its non-trivial band topology, and the resulted intriguing topological transport phenomena. In this study we report systematic electronic transport studies on tellurium flakes grown via a simple vapor deposition process. The sample is self-hole-doped, and exhibits typical weak localization behavior at low temperatures. Substantial negative longitudinal magnetoresistance under parallel magnetic field is observed over a wide temperature region, which is considered to share the same origin with that in tellurium bulk crystals, i.e., the Weyl points near the top of valence band. However, with lowering temperature the longitudinal magnetoconductivity experiences a transition from parabolic to linear field dependency, differing distinctly from the bulk counterparts. Further analysis reveals that such a modulation of Weyl behaviors in this low-dimensional tellurium structure can be attributed to the enhanced inter-valley scattering at low temperatures. Our results further extend Weyl physics into a low-dimensional semiconductor system, which may find its potential application in designing topological semiconductor devices.     

On the crossing of thin shells

The crossing of two dust shells is considered as a simplified model of a collapsing thick layer of dust. We use the Israel's formalism to describe the development of two shells of dust which interact only gravitationally. The formalism is developed in both Schwarzschild and Kruskal coordinates.     

Hydrothermal convection in moderately thin spherical shells

Hydrothermal convection of pore water with a temperature-dependent viscosity within a permeable, internally heated, moderately thin spherical shell is investigated by both a perturbation analysis and a direct numerical simulation. The analysis and simulation are mainly focused on a thin spherical shell in that convective instabilities are characterized by the spherical harmonic degree l=6 with a 13-fold mathematical degeneracy. Four different three-dimensional analytical solutions of convection are derived by removing the degeneracy through the nonlinear effect. A direct numerical simulation of the nonlinear problem is also carried out, showing satisfactory agreement between the analytical solutions and the numerical simulations.     

Maximal acceleration,maximal angular velocity,and causal influence

The upper bounds to acceleration and angular velocity which are suggested by quantum gravitational effects are described, together with the relativistic bound to velocity, by means of a cone ⁺ in the Lie algebra of the Poincaré group. The connection between these bounds and the existence of a minimal measurable length (of the order of Planck's length) is illustrated by means of a simple model. The geometric properties of the cone ⁺ and of other related structures are examined in some detail. The new geometric background requires some modifications of the concepts of causal influence and of spacetime coincidence, which are analyzed and shown to lead to some nonlocal features of the theory. Due to the smallness of Planck's length, these modifications to the causal relations cannot be observed by means of available experimental methods, but they could have some influence on the structure of elementary particles and on the very early cosmology.     

Dominant modes of submerged thin cylindrical shells

The relationship between the dominant mode of the submerged thin cylindrical shell and the flexural wave velocity is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, it is difficult to estimate the dominant mode, especially if two or more vibration modes are involved. To estimate the dominant mode of a thin shell in vacuo, the concept of “modified bending stiffness” has been introduced. In this paper, the concept of modified bending stiffness is extended to estimate the dominant mode of a submerged thin cylindrical shell. The dominant mode of a submerged thin cylindrical shell is theoretically discriminated from the other mode based on the smallness of the modified bending stiffness of the submerged shell. The validity of our theory is confirmed by a good agreement between theoretical and experimental results on flexural wave velocity.     

General theory of micropolar elastic thin shells

The paper formulates general hypotheses of micropolar elastic thin shells that are given asymptotic validation. Using these hypotheses and three-dimensional Cosserat (micropolar, asymmetric) theory of elasticity, general two-dimensional applied models of micropolar elastic thin shells with independent displacement and rotation fields, constrained rotation and low shear rigidity are constructed to suit dimensionless physical parameters of the shell material. The constructed micropolar shell models take into complete account transverse shear strain and related strain. Models of micropolar elastic thin plates and beams are particular cases of the constructed micropolar shell models. An axially symmetric stress-strain state problem of a hinged cylindrical micropolar shell is considered. Numerical analysis is used to demonstrate effective strength and rigidity characteristics of micropolar elastic shells.     

Stability of generic thin shells in conformally flat spacetimes

Some important spacetimes are conformally flat; examples are the Robertson–Walker cosmological metric, the Einstein–de Sitter spacetime, and the Levi-Civita–Bertotti–Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., \(p=\omega \sigma .\) It is shown that, for the physical domain of \(\omega \), i.e., \(0<\omega \le 1\), such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated.     

Laser acceleration of electrons in a thin metal film

A mechanism acceleration of electrons to relativistic velocities in a thin metal film irradiated with ultrashort (τ _L ≤1 ps) high-power (I>¹⁶ W/cm²) laser pulses is proposed. The acceleration is due to a resonance action of the nonuniform field on a portion of the electrons, viz., those which oscillate in the direction transverse to the film with a frequency close to the frequency of the field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 8–12 (10 July 1997)     

Enhanced ion acceleration with extremely thin foils

Enhanced backward-acceleration of ions is experimentally observed when ultra-short, high-intensity and ultra-high-contrast laser pulses interact with thin foils having thicknesses in the order of the penetration depth of the laser light. Below the experimentally observed optimum foil thickness for the maximum ion energy versus thickness, there arises a second peak. 1D simulations on foils with an initial plasma density gradient show a similar trend as the experiment. It appears that in this regime of extremely thin foils it is important to take into account the limited expansion of the plasma that is formed by ultra-high-contrast pulses.     

Maximal acceleration,Mach's principle,and the mass of the electron

Recent arguments for an upper limit to the proper acceleration of extended massive bodies are briefly reviewed. A transient mass shift in accelerated objects with non-constant proper mass density, expected in all locally Lorentz-invariant theories of gravitation which satisfy Mach's principle, is considered. This effect affects arguments for a maximal proper acceleration. It is shown that, while the widely discussed upper limit to proper acceleration obtains for rigid bodies with constant proper mass density, the limit ceases to obtain generally if this effect is taken into consideration. Applicability of maximal acceleration arguments to elementary particles is briefly considered in the context of a plausible classical model of the electron (one where the mass of the electron follows from the electronic charge).     

Asymptotic scaling laws for imploding thin fluid shells

Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the (A,M) parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A,M >1. It is shown that there exists a critical value gamma(cr) = 1+2/nu (nu = 1,2 for, respectively, cylindrical and spherical flows) of the adiabatic index gamma, which separates two qualitatively different patterns of the density buildup in the last phase of implosion. The scaling of the stagnation density rho(s) and pressure P(s) with the peak value M(0) of the Mach number is obtained.     

Problems with tunneling of thin shells from black holes

It is shown that exp(−2 Im(∫ p dr)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However, it is shown that this gives half the correct temperature for black holes.