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1

Green tensor and regular solutions of equations of rods thermodynamics and their properties

Alexeyeva Lyudmila, Dadayeva Assyat, Ainakeyeva Nursaule

Journal of Theoretical and Applied Mechanics

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2021

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Vol. 59 nr 2

227--238

EN

In the present paper, solutions of the equations of uncoupled thermoelastodynamics of ther- moelastic rods are constructed for power and thermal effects. Based on the Fourier transform, the Green tensor and generalized solutions of the thermoelasticity equations are constructed in the original space-time using the apparatus of generalized functions theory. Analytical formulas for definitions of the thermal stress-strain state of the rods taking into account its thermoelastic parameters are obtained. Shock thermoelastic waves are considered and con- ditions on their fronts are obtained. The results of numerical calculations of Green tensor are presented.

2

Green tensor in material sciences

Vlcek J., Otipka P.

Systemy Wspomagania w Inżynierii Produkcji

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2017

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Vol. 6, iss. 4

334--341

EN

Material properties of heterogeneous nanomaterials modelled by effective medium approximation (EMA) demand specific approaches when metallic inclusions in a host medium are exposed to external magnetic field. Resulting induced anisotropy of permittivity is manifested itself by a specific form of polarizability tensor. In presented work, this one is applied in the so called “strong-couple-dipole” (SCD) method, where the electromagnetic Green tensor is of key importance. The results are oriented to the magneto-plasmonic sensor element design for the use in biology or chemistry.

CS

Modelování materiálových vlastnosti heterogenních nanomateriálu metodou aproximace efektivním prostredím (EMA) vyžaduje specifický prístup, jsou-li kovové cástice v obklopujícím prostredí vystaveny magnetickému poli. Výsledná indukovaná anizotropie permitivity se projevuje specifickou formou tenzoru polarizovatelnosti. Ten je v této práci aplikován prostrednictvím tzv. metody silne vázaných dipólu (SCD), kde se klícovým zpusobem uplatnuje Greenuv (elektromagnetický) tenzor. Výsledky smerují k návrhu magneto-plasmonického senzoru s užitím v bilogii a chemii.

3

A second kind integral equation formulation for the interaction between a solid particle and a compound drop at low Reynolds number

Kohr M.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 3

557-577

EN

In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.

4

An integral method for two-dimensional stokes flows past rigid obstacles in the half-plane

Kohr M.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 1

5-24

EN

The problem of determining the slow viscous flow of a fluid past a cylinder with an arbitrary cross section, in a domain with boundary limited by a plane wall, is formulated as a system of Fredholm linear integral equations of the second kind. We next complete the double-layer potentials of the system with some terms having singularities located inside the obstacle and which satisfy the nonslip boundary condition on the wall. We next prove that this system of integral equations has a unique continuous solution when the boundary of the particle is a Lyapunov curve. Also, the numerical results are given for the case of a fixed circular obstacle. For the numerical solution we use a standard boundary element technique.