scholarly journals The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jerry P. Selvaggi ◽  
Jerry A. Selvaggi
Keyword(s):  
Analytical Approach ◽  
Integration Process ◽  
Convolution Integral ◽  
The Real ◽  
Dirac Type ◽  
Convolution Integrals ◽  
Full Power ◽  
Integrated Or ◽  
Bose Einstein ◽  
Laplace Transform Inversion

The Fermi-Dirac-type or Bose-Einstein-type integrals can be transformed into two convergent real-convolution integrals. The transformation simplifies the integration process and may ultimately produce a complete analytical solution without recourse to any mathematical approximations. The real-convolution integrals can either be directly integrated or be transformed into the Laplace Transform inversion integral in which case the full power of contour integration becomes available. Which method is employed is dependent upon the complexity of the real-convolution integral. A number of examples are introduced which will illustrate the efficacy of the analytical approach.

scholarly journals Lp-valued stochastic convolution integral driven by Volterra noise

2018 ◽  
Vol 18 (06) ◽  
pp. 1850048 ◽  
Author(s):  
Petr Čoupek ◽  
Bohdan Maslowski ◽  
Martin Ondreját
Keyword(s):  
Banach Space ◽  
State Space ◽  
Stochastic Partial Differential Equations ◽  
Main Tool ◽  
Space Time ◽  
Convolution Integral ◽  
Hölder Continuous ◽  
Stochastic Convolution ◽  
Wiener Chaos ◽  
Convolution Integrals

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space [Formula: see text]. The corresponding regularity is obtained by showing that the stochastic convolution integrals are Hölder continuous in a suitable function space. In particular cases, this allows us to show space-time Hölder continuity of the solution. The main tool used is a hypercontractivity result on Banach-space valued random variables in a finite Wiener chaos.

ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

2012 ◽  
Vol 63 (1) ◽  
pp. 187-211 ◽  
Author(s):  
Luisa D’Amore ◽  
Rosanna Campagna ◽  
Valeria Mele ◽  
Almerico Murli
Keyword(s):  
Laplace Transform ◽  
Software Package ◽  
The Real ◽  
Laplace Transform Inversion

scholarly journals Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

2013 ◽  
Vol 63 (3) ◽  
pp. 571-571
Author(s):  
Luisa D’Amore ◽  
Rosanna Campagna ◽  
Valeria Mele ◽  
Almerico Murli ◽  
Mariarosaria Rizzardi
Keyword(s):  
Laplace Transform ◽  
Software Package ◽  
The Real ◽  
Laplace Transform Inversion

Laplace transform inversion on the real line is truly ill-conditioned

2013 ◽  
Vol 219 (18) ◽  
pp. 9805-9809 ◽  
Author(s):  
H. Gzyl ◽  
A. Tagliani ◽  
M. Milev
Keyword(s):  
Laplace Transform ◽  
Real Line ◽  
The Real ◽  
Laplace Transform Inversion

scholarly journals Spatial separation of degenerate components of magnon Bose–Einstein condensate by using a local acceleration potential

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
I. V. Borisenko ◽  
V. E. Demidov ◽  
V. L. Pokrovsky ◽  
S. O. Demokritov
Keyword(s):  
Room Temperature ◽  
Phase Locking ◽  
Minimum Energy ◽  
Spatial Separation ◽  
Real Space ◽  
Einstein Condensate ◽  
Quantized Vortices ◽  
Einstein Condensation ◽  
The Real ◽  
Bose Einstein

Abstract Bose–Einstein condensation (BEC) of magnons is one of the few macroscopic quantum phenomena observable at room temperature. Due to the competition of the exchange and the magnetic dipole interactions, the minimum-energy magnon state is doubly degenerate and corresponds to two antiparallel non-zero wavevectors. Correspondingly, the room-temperature magnon BEC differs essentially from other condensates, since it takes place simultaneously at ± kmin. The degeneracy of BEC and interaction between its two components have significant impact on condensate properties. Phase locking of the two condensates causes formation of a standing wave of the condensate density and quantized vortices. Additionally, interaction between the two components is believed to be important for stabilization of the condensate with respect to a real-space collapse. Thus, the possibility to create a non-degenerate, single-component condensate is decisive for understanding of underlying physics of magnon BEC. Here, we experimentally demonstrate an approach, which allows one to accomplish this challenging task. We show that this can be achieved by using a separation of the two components of the degenerate condensate in the real space by applying a local pulsed magnetic field, which causes their motion in the opposite directions. Thus, after a certain delay, the two clouds corresponding to different components become well separated in the real space. We find that motion of the clouds can be described well based on the peculiarities of magnon dispersion characteristics. Additionally, we show that, during the motion, the condensate cloud harvests non-condensed magnons, which results in a partial compensation of condensate depletion.

scholarly journals Convolution Integral: How a Graphical Type of Solution Can Help Minimize Misconceptions

2021 ◽  
Vol 3 (2) ◽  
pp. 103
Author(s):  
Hendra J. Tarigan
Keyword(s):  
Impulse Response ◽  
Physical System ◽  
Convolution Integral ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Convolution Integrals ◽  
Low Pass ◽  
Simulation And Experiment ◽  
Rc Circuit ◽  
Set Up

A physical system, Low Pass Filter (LPF) RC Circuit, which serves as an impulse response and a square wave input signal are utilized to derive the continuous time convolution (convolution integrals). How to set up the limits of integration correctly and how the excitation source convolves with the impulse response are explained using a graphical type of solution. This in turn, help minimize the students’ misconceptions about the convolution integral. Further, the effect of varying the circuit elements on the shape of the convolution output plot is presented allowing students to see the connection between a convolution integral and a physical system. PSpice simulation and experiment results are incorporated and are compared with those of the analytical solution associated with the convolution integral.

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