On $$\mathbb {R}$$-Linear Problem and Truncated Wiener–Hopf Equation

2020 ◽  
Vol 30 (2) ◽  
pp. 143-151
Author(s):  
A. F. Voronin
Keyword(s):  
Linear Problem ◽  
Hopf Equation

Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

2020 ◽  
Vol 13 (3) ◽  
pp. 143-161
Author(s):  
M.V. Dudyk
Keyword(s):  
Contact Area ◽  
Fracture Zone ◽  
Mutual Influence ◽  
Interfacial Crack ◽  
Normal Displacement ◽  
Crack Model ◽  
Hopf Equation ◽  
Resistant Material ◽  
Order Of Magnitude ◽  
Crack Faces

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.

scholarly journals Cooperative Operation Schedules of Energy Storage System and Demand Response Resources Considering Urban Railway Load Characteristic under a Time-of-Use Tariff

2021 ◽  
Vol 16 (3) ◽  
pp. 1273-1284
Author(s):  
Hye Ji Kim ◽  
Hosung Jung ◽  
Young Jun Ko ◽  
Eun Su Chae ◽  
Hyo Jin Kim ◽  
...  
Keyword(s):  
Energy Storage ◽  
Demand Response ◽  
Air Conditioning ◽  
Linear Problem ◽  
Storage System ◽  
Energy Charge ◽  
Energy Storage System ◽  
Peak Reduction ◽  
Railway Stations ◽  
Charging And Discharging Processes

AbstractThis paper proposes an algorithm for the cooperative operation of air conditioning facilities and the energy storage system (ESS) in railway stations to minimize electricity. Unlike traditional load patterns, load patterns of an urban railway station can peak where energy charge rates are not high. Due to this possibility, if applying the traditional peak-reduction algorithm to railway loads, energy changes can increase, resulting in higher electricity bills. Therefore, it is required to develop a new method for minimizing the sum of capacity charges and energy charges, which is a non-linear problem. To get a feasible solution for this problem, we suggest an algorithm that optimizes the facility operation through two optimizations (primary and secondary). This method is applied to the air-quality change model for operating air conditioning facilities as demand-response (DR) resources in railway stations. This algorithm makes it possible to estimate operable DR capacity every hour, rather than calculating the capacity of DR resources conservatively in advance. Finally, we perform a simulation for the application of the proposed method to the operation of DR resources and ESS together. The simulation shows that electricity bills become lowered, and the number of charging and discharging processes of ESS is also reduced.

A Contingency Perspective on Effective Prototyping

1993 ◽  
Vol 8 (2) ◽  
pp. 99-109
Author(s):  
Oscar Gutierrez
Keyword(s):  
Project Management ◽  
Problem Solving ◽  
Organizational Support ◽  
Linear Problem ◽  
Systems Development ◽  
Social Mechanism ◽  
Contingency Perspective ◽  
Future Developments ◽  
Product And Process ◽  
Selection Of

Current demands on prototyping emphasize increasingly complex and dynamic applications that require sophisticated social mechanism and process enablers. However, much of the emphasis placed today in systems development under prototyping focuses on the supporting technology. The imbalance between product and process perspectives under this approach is explored. A view of prototyping effectiveness is presented in terms of non-linear problem solving, adequate technical and procedural solutions, and organizational support. Implications of this view are presented on the selection of prototyping techniques and on project management concerns. Future developments in prototyping practice are explored.

scholarly journals Instability, nonexistence, and uniqueness in elasticity with porous dissipation

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
M. C. Leseduarte ◽  
R. Quintanilla
Keyword(s):  
Nonlinear Problem ◽  
Exponential Growth ◽  
Linear Problem ◽  
Linear Equations ◽  
Uniqueness Of Solutions ◽  
Time Problem ◽  
Nonexistence Of Solutions

This paper is devoted to the study of the elasticity with porous dissipation. In the context of the nonlinear problem, we prove instability and nonexistence of solutions. In the context of the linear problem, we obtain exponential growth. We also obtain uniqueness of solutions of the backward in time problem of the linear equations.

The effect of a singular term in a quadratic quasi-linear problem

2016 ◽  
Vol 19 (1) ◽  
pp. 815-831 ◽  
Author(s):  
David Arcoya ◽  
Lourdes Moreno-Mérida
Keyword(s):  
Linear Problem ◽  
Singular Term

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

On the scattering of sound by two semi-infinite parallel staggered plates - I. Explicit matrix Wiener-Hopf factorization

1988 ◽  
Vol 420 (1858) ◽  
pp. 131-156 ◽  
Keyword(s):  
Asymptotic Expression ◽  
Series Representation ◽  
Auxiliary Function ◽  
Sound Waves ◽  
Parallel Plates ◽  
Hopf Equation ◽  
Product Decomposition ◽  
Matrix Kernel ◽  
Wave Fields ◽  
The Matrix

This paper discusses the two-dimensional scattering of sound waves by two semi-infinite rigid parallel plates. The plates are staggered, so that a line in the plane of the motion passing through both edges is not in general perpendicular to the plane of either plate. The problem is formulated as a matrix Wiener-Hopf functional equation, which exhibits the difficulty of a kernel containing exponentially growing elements. We show how this difficulty may be overcome by constructing an explicit product decomposition of the matrix kernel with both factors having algebraic behaviour at infinity. This factorization is written in terms of a single entire auxiliary function that has a simple infinite series representation. The Wiener-Hopf equation is solved for arbitrary incident wave fields and we derive an asymptotic expression for the field scattered to infinity; the latter includes the possibility of propagating modes in the region between the plates. In part II of this work we will evaluate our solution numerically and obtain some analytical estimates in a number of physically interesting limits.

Asymptotic analysis of some two-dimensional diffusion problems

1995 ◽  
Vol 448 (1933) ◽  
pp. 213-236 ◽  
Keyword(s):  
Linear Problem ◽  
Vacancy Concentration ◽  
Surface Concentration ◽  
Two Dimensional ◽  
Surface Source ◽  
Dimensional Diffusion ◽  
Equilibrium Vacancy ◽  
Equilibrium Vacancy Concentration ◽  
Dimensional Surface ◽  
Diffusion Problems

In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a va­cancy model.

Cauchy problems involving a Hadamard-type fractional derivative

2018 ◽  
Vol 68 (6) ◽  
pp. 1353-1366
Author(s):  
Rafał Kamocki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Unique Solution ◽  
Nonlinear Problem ◽  
Point Theorem ◽  
Linear Problem ◽  
Cauchy Formula ◽  
Cauchy Problems

Abstract In this paper, we investigate some Cauchy problems involving a left-sided Hadamard-type fractional derivative. A theorem on the existence of a unique solution to a nonlinear problem is proved. The main result is obtained using a fixed point theorem due to Banach, as well as the Bielecki norm. A Cauchy formula for the solution of the linear problem is derived.

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