scholarly journals Arrays of Sub-Terahertz Cryogenic Metamaterial

2021 ◽  
Vol 11 (20) ◽  
pp. 9649
Author(s):  
Mikhail Tarasov ◽  
Aleksandra Gunbina ◽  
Artem Chekushkin ◽  
Vyacheslav Vdovin ◽  
Aleksei Kalaboukhov
Keyword(s):  
Boundary Conditions ◽  
Antenna Arrays ◽  
Periodic Boundary ◽  
Spectral Characteristics ◽  
Periodic Boundary Conditions ◽  
Optical Filters ◽  
Complete Analysis ◽  
Phased Array Antenna ◽  
Detector Arrays ◽  
Lift Off

Integrated quasi-optical cryogenic terahertz receivers contain arrays of detectors, quasi-optical filters, interferometers, and other metamaterials. Matrices of quasi-optical band-pass, low-pass, and high-pass filters, Fabry–Perot grid interferometers, and arrays of half-wave and electrically small antennas with superconductor-insulator-normal metal-insulator-superconductor (SINIS) sub-terahertz wavelength range detectors were fabricated and experimentally studied on the same computational, technological, and experimental platform. For the design of the filters, we used the periodic frequency-selective surfaces (FSS) approach, contrary to detector arrays that can be presented in a model of distributed absorbers. The structures were fabricated using direct electron beam lithography, thermal shadow evaporation, lift-off, alternatively magnetron sputtering, and chemical and plasma etching. The numerical simulation methods of such structures are sufficiently different: for the reactive matrices with low losses, the approximation of an infinite structure with periodic boundary conditions is applicable, and for the arrays of detectors with dissipative elements of absorbers, a complete analysis of the finite structure with hundreds of interacting ports is applicable. The difference is determined by the presence of dissipation in the detector arrays, the phase of the reflected or re-emitted signal turned out to be undefined and the Floquet periodic boundary conditions are correct only for a phased array antenna. The spectral characteristics of the created filters, interferometers, and antenna arrays were measured in the frequency range 50–600 GHz.

scholarly journals Numerical Simulation of 3D Flow over a Circular Cylinder

2021 ◽  
Vol 2057 (1) ◽  
pp. 012072
Author(s):  
A N Kusyumov ◽  
S A Kusyumov ◽  
S A Mikhailov ◽  
E V Romanova
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Spectral Characteristics ◽  
Periodic Boundary Conditions ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
3D Flow ◽  
Navier Stokes Equations

Abstract Unsteady 3D flow over a circular cylinder at Reynolds number of 3900 is studied numerically using the Navier-Stokes equations. Two formulations of the problem were considered: with boundary conditions corresponding to the flow around an isolated cylinder and with periodic boundary conditions to the flow behind a parallel circular cylinders grid. A comparative analysis of the integral and distributed characteristics of the flow around the cylinder and the spectral characteristics of the flow for both formulations of the problem is carried out.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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