Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Anti-Stokes Bands of Intrinsic Radiation in Undoped GaAs Crystals

It has been established that undoped gallium crystals exhibit anti-Stokes radiation with energy corresponding to the interband recombination of these crystals. Its appearance is most probably determined by EL2 defects, and its intensity depends on the product of the cross sections for photoionization of electrons and the holes from these defects.     

Lorentz Invariant Decompositions of the State Vector Spaces and the Basis Problem

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together.     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

PURE STATE APPROACH TO $C(X)×_\alpha Z_n$

ＰＵＲＥ ＳＴＡＴＥ ＡＰＰＲＯＡＣＨ ＴＯ Ｃ（ｘ）_αＺ_nＬＩＢＩＮＧＲＥＮ；ＬＩＮＱＩＮＧ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ．Ｐｒｏｊｅｃｔｓｕｐｐｏｒｔｅｄｂｙｔｈ?..     

New developments in the field of piezothermal analysis

The solid transitions of C₂₁, C₂₃ and C₂₅ n-paraffins are examined from a piezothermal point of view. The paper is divided into two parts. The first is a report of the main features of a piezothermal analyzer when pressure scanning allows the continuous record of the expansivity as a function of pressure up to 5 Kilobars. Small samples are required and the scanning speeds vary from 0.3 to 16 Kilobars per hour. The second part describes the experimental procedure appropriate for solid state determinations. The resulting piezothermograms are presented and entropies of transformation are determined. A model allows a crude statistical approach giving the entropies of transformation with the correct order of magnitude. Problems related with phase transformations under a shearing stress are considered.

---

Zusammenfassung Feststoffumwandlungen bei C₂₁, C₂₃ und C₂₅ n-Paraffinen wurden unter dem Gesichtspunkt der Piezowärme untersucht. Im ersten Teil vorliegender Arbeit werden die Haupteigenschaften eines piezothermischen Analysators beschrieben, bei dem durch Druck-Scanning die kontinuierliche Aufzeichnung des Ausdehnungsvermögens als Punktion des Druckes bis zu 5 kbar ermöglicht wird. Es werden nur kleine Proben benötigt, die Scanning-Geschwindigkeit variiert zwischen 0,3 und 16 kbar/h. Der zweite Teil beschreibt das geeignete experimentelle Verfahren zur Feststoffzustandsbestimmung. Die erhaltenen Piezothermogramme werden dargestellt und die Entropien der Umwandlung bestimmt. Ein Modell liefert eine grobe statistische Näherung, die die Entropien der Umwandlung in der richtigen Grö\enordnung liefert. Probleme in Zusammenhang mit Phasenumwandlungen bei Scherbeanspruchungen werden betrachtet.

     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Topochemically Controlled Redox Reactions in the System In/Sn/Cl

The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl₂ is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl.     

Sequential nonlinear estimation with nonaugmented priors

How can the basic compatibility of theory and observations be investigated for nonlinear processes without requiring stochastic characterizations for residual error terms? The present paper proposes a flexible least-cost approach. For each possible estimatex for the sequence of process states, letc _D (x) andx _M(x) denote the costs incurred for deviations away from the prior dynamic specifications and prior measurement specifications, respectively. Define the cost-efficiency frontier to be the greatest lower bound for the set of all possible cost pairs [c _D (x),c _M(x)], conditional on the given observations. State sequence estimatesx that attain the cost-efficiency frontier indicate the possible ways that the actual process could have developed over time in a manner minimally incompatible with the prior dynamic and measurement specifications. An algorithm is developed for the exact sequential updating of the cost-efficient state sequence estimates as the duration of the process increases and additional observations are obtained.