Thermodynamic Approach to Generalized Continua

Governing equations of dissipative generalized solid mechanics are derived by thermodynamic methods in the Piola-Kirchhoff framework using the Liu procedure. The isotropic small strain case is investigated in more detail. The connection to the Ginzburg-Landau type evolution, dual internal variables, and a thermodynamic generalization of the standard linear solid model of rheology is demonstrated. Specific examples are chosen to emphasize experimental confirmations and predictions beyond less general approaches.Comment: 23 pages, sign error revisio

A New Redshift Interpretation

A nonhomogeneous universe with vacuum energy, but without spacetime expansion, is utilized together with gravitational and Doppler redshifts as the basis for proposing a new interpretation of the Hubble relation and the 2.7K Cosmic Blackbody Radiation.Comment: 9 pages LaTeX, no figure

Qualitative properties in strain gradient thermoelasticity with microtemperatures

This paper is devoted to the strain gradient theory of thermoelastic aterials whose microelements possess microtemperatures. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level. In the first part of this paper we deduce the system of basic equations of the linear theory and formulate the boundary-initial-value problem. We establish existence, uniqueness, and continuous dependence results by the means of semigroup theory. Then, we study the one-dimensional problem and establish the analyticity of solutions. Exponential stability and impossibility of localization are consequences of this result. In the case of the anti-plane problem we derive uniqueness and instability results without assuming the positivity of the mechanical energy. Finally, we study equilibrium theory and investigate the effects of a concentrated heat source in an unbounded bodyPeer ReviewedPostprint (author's final draft

The effects of random path fluctuations on the accuracy of laser ranging systems

The precision of satellite ranging systems, limited in part by atmospheric refraction and scattering, is examined. The effects of atmospheric turbulence on the accuracy of single color and multicolor ranging systems is discussed. The statistical characteristics of the random path length fluctuations induced by turbulence are examined. Correlation and structure functions are derived using several proposed models for the variations of the optical path length. For single color systems it is shown that the random path length fluctuations can limit the accuracy of a range measurement to a few centimeters. Two color systems can partially correct for the random path fluctuations so that in most cases their accuracy is limited to a few millimeters. However, at low elevation angles and over long horizontal paths two color systems can also have errors approaching a few centimeters

The stellar scintillation on large and extremely large telescopes

The accuracy of ground-based astronomical photometry is limited by two factors: photon statistics and stellar scintillation arising when star light passes through Earth's atmosphere. This paper examines the theoretical role of the outer scale $L_0$ of the optical turbulence (OT) which suppresses the low-frequency component of scintillation. It is shown that for typical values of $L_0 \sim 25 - 50$ m, this effect becomes noticeable for a telescopes of diameter around 4 m. On extremely large, $30 - 40$ m, telescopes with exposures longer than a few seconds, the inclusion of the outer scale in the calculation reduces the scintillation power by more than a factor of 10 relative to conventional estimates. The details of this phenomenon are discussed for various models of non-Kolmogorov turbulence. Also, a quantitative description of the influence of the telescope central obscuration on the measured scintillation noise is introduced and combined with the effect of the outer scale. Evaluation of the scintillation noise on the future TMT and E-ELT telescopes, predicts an amplitude of approximately 10 \mumag for a 60 s exposures.Comment: Accepted for publication in MNRAS, 10 pages, 9 figure

On the stabilization of a thermoelastic laminated beam system with microtemperature effects

The present article investigates a one-dimensional thermoelastic laminated beam with microtemperature effects. Using the energy method, we prove in the case of zero thermal conductivity that the unique dissipation due to the microtemperatures is strong enough to exponentially stabilize the system if and only if the wave speeds of the system are equal. Our result is new and improves previous results in the literature. Mathematics Subject Classification (2010): 35B40, 74F05, 93D15, 93D20. Received 22 October 2024; Accepted 28 February 2025