Description of the short-term process by the equation of heat conductivity with fractional derivatives

2020 ◽  
pp. 7-19
Author(s):  
Yu.A. Kirsanov ◽  
◽  
A.Yu. Kirsanov ◽  
Keyword(s):  
Fractional Derivatives ◽  
Differential Operators ◽  
Thermal Relaxation ◽  
Heat Conducting ◽  
Short Term ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
The Third ◽  
Derivatives Of ◽  
Conductivity Models

The thermal conductivity models of Fourier, Cattaneo-Vernotte, Maxwell-Cattaneo-Luikov and models with fractional time derivatives of temperature and heat flux are considered. An algorithm for the numerical solution of the generalized problem of one-dimensional heat conduction is constructed. The algorithm comprises all the models listed above applying boundary conditions of the third kind and difference analogs of differential operators of the second order of accuracy in coordinate and time. The parameters (Biot number, time of thermal relaxation and thermal damping, indicators of fractional derivatives) that describe experimental transient processes are determined using the listed models applied for both in the center and on the surface of a low heat-conducting body.

Fractional derivatives of multidimensional Colombeau generalized stochastic processes

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Danijela Rajter-Ćirić ◽  
Mirjana Stojanović
Keyword(s):  
Stochastic Process ◽  
Fractional Derivative ◽  
Stochastic Processes ◽  
Compact Support ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
One Dimensional ◽  
Compactly Supported ◽  
Derivatives Of ◽  
Do So

AbstractWe consider fractional derivatives of a Colombeau generalized stochastic process G defined on ℝn. We first introduce the Caputo fractional derivative of a one-dimensional Colombeau generalized stochastic process and then generalize the procedure to the Caputo partial fractional derivatives of a multidimensional Colombeau generalized stochastic process. To do so, the Colombeau generalized stochastic process G has to have a compact support. We prove that an arbitrary Caputo partial fractional derivative of a compactly supported Colombeau generalized stochastic process is a Colombeau generalized stochastic process itself, but not necessarily with a compact support.

Heat Kernel Expansions in the Case of Conic Singularities

2003 ◽  
Vol 18 (12) ◽  
pp. 2197-2203 ◽  
Author(s):  
R. Seeley
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Zeta Function ◽  
Differential Operators ◽  
Smooth Boundary ◽  
General Nature ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
The Third ◽  
Elliptic Differential Operators

For positive elliptic differential operators Δ, the asymptotic expansion of the heat trace tr(e-tΔ) and its related zeta function ζ(s, Δ) = tr(Δ-s) have numerous applications in geometry and physics. This article discusses the general nature of the boundary conditions that must be considered when there is a singular stratum, and presents three examples in which a choice of boundary conditions at the singularity must be made. The first example concerns the signature operator on a manifold with a singular stratum of conic type. The second concerns the "Zaremba problem" for a nonsingular manifold with smooth boundary, posing Dirichlet conditions on part of the boundary and Neumann conditions on the complement; the intersection of these two regions can be viewed as a singular stratum of conic type, and a boundary condition must be imposed along this stratum. The third example is a one-dimensional manifold where the operator at one end has a singularity like that in conic problems, and the choice of boundary conditions affects not just the residues at the poles of the zeta function, but also the very location of the poles

scholarly journals Immersed Interface CIP for One Dimensional Hyperbolic Equations

2014 ◽  
Vol 16 (1) ◽  
pp. 96-114
Author(s):  
Kazufumi Ito ◽  
Tomoya Takeuchi
Keyword(s):  
Hyperbolic Equations ◽  
Third Order ◽  
Immersed Interface ◽  
Order Of Accuracy ◽  
Piecewise Constant ◽  
One Dimensional ◽  
The Third ◽  
Numerical Tests ◽  
Jump Discontinuities ◽  
Constant Coefficients

AbstractThe immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method.

scholarly journals From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

2003 ◽  
Vol 18 (19) ◽  
pp. 3347-3368 ◽  
Author(s):  
A. Bouda
Keyword(s):  
Kinetic Term ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Classical Potential ◽  
The One ◽  
Quantum Motion ◽  
Derivatives Of ◽  
Hamilton Jacobi Equation

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a nonrelativistic spinless system. This Lagrangian is written as a difference between a function T, which represents the quantum generalization of the kinetic energy and which depends on the coordinate x and the temporal derivatives of x up the third order, and the classical potential V(x). The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function T is first assumed to be arbitrary. The development of T in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton–Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton law. We also analytically establish the famous Bohm relation [Formula: see text] outside the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, plays really the role of an additional potential as assumed by Bohm.

scholarly journals Fractional Derivative Regularization in QFT

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Euclidean Space ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Regularization Procedure ◽  
Derivatives Of ◽  
Massless Fields

We propose in this paper a new regularization, where integer-order differential operators are replaced by fractional-order operators. Regularization for quantum field theories based on application of the Riesz fractional derivatives of noninteger orders is suggested. The regularized loop integrals depend on parameter that is the order α>0 of the fractional derivative. The regularization procedure is demonstrated for scalar massless fields in φ4-theory on n-dimensional pseudo-Euclidean space-time.

scholarly journals REGULAR FRACTIONAL DIRAC TYPE SYSTEMS

2021 ◽  
pp. 489
Author(s):  
Bilender P Allahverdiev ◽  
Huseyin Tuna
Keyword(s):  
Fractional Derivatives ◽  
Type Systems ◽  
One Dimensional ◽  
Dirac Type ◽  
The Right ◽  
Derivatives Of

In this paper, we study one dimensional fractional Dirac type systems which includes the right-sided Caputo and the left-sided Riemann-Liouvile fractional derivatives of same order α,α∈(0,1). We investigate the properties of the eigenvalues and the eigenfunctions of this system

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

scholarly journals Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 475
Author(s):  
Ewa Piotrowska ◽  
Krzysztof Rogowski
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Electric Circuit ◽  
Theoretical Models ◽  
Time Domain Analysis ◽  
Electrical Circuit ◽  
State Variable ◽  
State Space System ◽  
Derivatives Of ◽  
Different Order

The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and capacitances. Different orders of differentiation lead to the state-space system model, in which each state variable has a different order of fractional derivative. Solutions for such models are presented for three cases of derivative operators: Classical (first-order differentiation), Caputo definition, and Conformable Fractional Derivative (CFD). Using theoretical models, the step responses of the fractional electrical circuit were computed and compared with the measurements of a real electrical system.

scholarly journals Cost-effectiveness of a hybrid emergency room system for severe trauma: a health technology assessment from the perspective of the third-party payer in Japan

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Takahiro Kinoshita ◽  
Kensuke Moriwaki ◽  
Nao Hanaki ◽  
Tetsuhisa Kitamura ◽  
Kazuma Yamakawa ◽  
...  
Keyword(s):  
Cost Effectiveness ◽  
Emergency Room ◽  
Healthcare Costs ◽  
Cost Effective ◽  
Severe Trauma ◽  
Third Party ◽  
Trauma Patients ◽  
Short Term ◽  
The Third

Abstract Background Hybrid emergency room (ER) systems, consisting of an angiography-computed tomography (CT) machine in a trauma resuscitation room, are reported to be effective for reducing death from exsanguination in trauma patients. We aimed to investigate the cost-effectiveness of a hybrid ER system in severe trauma patients without severe traumatic brain injury (TBI). Methods We conducted a cost-utility analysis comparing the hybrid ER system to the conventional ER system from the perspective of the third-party healthcare payer in Japan. A short-term decision tree and a long-term Markov model using a lifetime time horizon were constructed to estimate quality-adjusted life years (QALYs) and associated lifetime healthcare costs. Short-term mortality and healthcare costs were derived from medical records and claims data in a tertiary care hospital with a hybrid ER. Long-term mortality and utilities were extrapolated from the literature. The willingness-to-pay threshold was set at $47,619 per QALY gained and the discount rate was 2%. Deterministic and probabilistic sensitivity analyses were conducted. Results The hybrid ER system was associated with a gain of 1.03 QALYs and an increment of $33,591 lifetime costs compared to the conventional ER system, resulting in an ICER of $32,522 per QALY gained. The ICER was lower than the willingness-to-pay threshold if the odds ratio of 28-day mortality was < 0.66. Probabilistic sensitivity analysis indicated that the hybrid ER system was cost-effective with a 79.3% probability. Conclusion The present study suggested that the hybrid ER system is a likely cost-effective strategy for treating severe trauma patients without severe TBI.

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