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The Euclidean space, obtained by the analytical continuation of time, to an imaginary time, is used to model thermal systems. In this work, it is taken a step further to systems with spatial thermal variation, by developing an equivalence between the spatial variation of temperature in a thermal bath and the curvature of the Euclidean space. The variation in temperature is recast as a variation in the metric, leading to a curved Euclidean space. The equivalence is substantiated by analyzing the Polyakov loop, the partition function and the periodicity of the correlation function. The bulk thermodynamic properties like the energy, entropy and the Helmholtz free energy are calculated from the partition function, for small metric perturbations, for a neutral scalar field. The Dirac equation for an external Dirac spinor, traversing a thermal bath with spatial thermal gradients, is solved in the curved Euclidean space. The fundamental behavior exhibited by the Dirac spinor eigenstate, may provide a possible mechanism to validate the theory, at a more basal level, than examining only bulk thermodynamic properties. Furthermore, in order to verify the equivalence at the level of classical mechanics, the geodesic equation is analyzed in a classical backdrop. The mathematical apparatus is borrowed from the physics of quantum theory in a gravity-induced space–time curvature. As spatial thermal variations are obtainable at quantum chromodynamic or quantum electrodynamic energies, it may be feasible for the proposed formulation to be validated experimentally.

The steady-state force on the droplet released in another liquid subjected to the gravitational field and imposed thermal gradient in the case of vanishingly small Re and Ma is derived using the general solution given by Lamb. A solution to a transitional thermocapillary-type droplet migration is thereby obtained for the case of constant physical properties, which corresponds to the well known YGB result as t → ∞. These can be employed to investigate the interactions between droplets in a host solution under the gravitational and thermal influences, and further to explore deposition and migration of a droplet cluster in the corresponding fields.

In this paper, we investigate the magnetic-domain wall (DW) dynamics in uniaxial/biaxial-nanowires under a thermal gradient (TG). The findings reveal that the DW propagates toward the hotter region in both nanowires. In uniaxial nanowire, the DW propagates accompanying a rotation of the DW-plane. In biaxial nanowire, the DW propagates in the hotter region, and the so-called Walker breakdown phenomenon is observed. The main physics of such DW dynamics is the magnonic angular momentum transfer to the DW. The hard (shape) anisotropy exists in biaxial-nanowire, which contributes an additional torque; hence DW speed is larger than that in uniaxial-nanowire. But the rotational speed is lower initially as hard anisotropy suppresses the DW-rotation. After certain TG, DW-plane overcomes the hard anisotropy and so the rotational speed increases slightly. With lower damping, the DW velocity is smaller and DW velocity increases with damping which is a contrary to usual desire. The reason is predicted as the formation of the standing spin-waves (by superposing the spin waves and its reflection from the boundary) which do not carry any net energy to DW. However, for larger damping, DW velocity decreases with damping since the magnon-propagation length decreases. Therefore, the above findings might be useful to realize the spintronics (i.e. racetrack-memory) devices.

Based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method, we investigated how the thermal gradient affects the vibration behavior of rotating isotropic and orthotropic oval cylindrical shells. The governing equations of orthotropic oval cylindrical shells, under parabolically varying thermal gradient around its circumference, with consideration of the effects of initial hoop tension and centrifugal forces due to the rotation are derived, and they are put in a matrix differential equation as a boundary-value problem. As a semianalytic solution, the trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction, and also to reduce the two-dimensional problem in to an one-dimensional one. Using the transfer matrix approach, the equations can be written in a matrix differential equation of first-order and solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and vibratory displacement of the symmetrical and antisymmetrical vibration modes. The sensitivity of the vibration behavior to the rotational speed, the thermal gradient, the ovality and orthotropy of the shell is studied for different type-modes of vibration. The present method is found to be accurate when compared with the results available in the literature.

Metal matrix composites (MMCs) are regarded to be one of the most principal classifications in composite materials. The thermal characterization of hybrid MMCs has become increasingly important in a wide range of applications. Thermal conductivity is one of the most important properties of MMCs. Since nearly all MMCs are used in various temperature ranges, measurement of thermal conductivity as a function of temperature is necessary in order to know the behavior of the material. In the present research, evaluation of thermal conductivity has been accomplished for aluminum alloy (Al) 6061, silicon carbide (SiC) and graphite (Gr) hybrid MMCs from room temperature to $300^{\circ }$C. Al-based composites reinforced with SiC and Gr particles have been prepared by stir casting technique. The thermal conductivity behavior of hybrid composites with different percentage compositions of reinforcements has been investigated using laser flash technique. The results have indicated that the thermal conductivity of the different compositions of hybrid MMCs decreases by the addition of Gr with SiC and Al 6061. Few empirical models have been validated concerning with the evaluation of thermal conductivity of composites. Using the experimental values namely density, thermal conductivity, specific heat capacity and enthalpy at varying temperature ranges, computational investigation has been carried out to evaluate the thermal gradient and thermal flux.