Development and Calculation of a Computer Model and Modern Distributed Algorithms for Dispersed Systems Aggregation

2020 ◽  
Vol 11 (2) ◽  
pp. 56-68
Author(s):  
Nurlybek Zhumatayev ◽  
Zhanat Umarova ◽  
Gani Besbayev ◽  
Almira Zholshiyeva
Keyword(s):  
Distributed Algorithms ◽  
Computer Model ◽  
Initial Conditions ◽  
Relaxation Times ◽  
Calculation Algorithm ◽  
Dispersed Systems ◽  
Perfect Model ◽  
Aggregation Processes ◽  
Non Local ◽  
Non Local Equations

In this work, an attempt has been made to eliminate the contradiction of the Smoluchowski equation, using modern distributed algorithms for creating calculation algorithm and implementation a program for building a more perfect model by changing the type of the kinetic equation of aggregation taking into account the relaxation times. On the basis of the applied Mathcad package, there is a developed computer model for calculating the aggregation of dispersed systems. The obtained system of differential equations of the second order is solved by the Runge-Kutt method. The authors are presetting the initial conditions of the calculation. A subsequent analysis was made of the obtained non-local equations and the study of the behavior of solutions of different orders. Also, this research can be aimed at the generalization of the proposed approach for the analysis of aggregation processes in heterogeneous dispersed systems, involving the creation of aggregation models, taking into account both time and space non-locality.

scholarly journals Replica wormholes for an evaporating 2D black hole

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kanato Goto ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Path Integral ◽  
Island Rule ◽  
Technical Challenge ◽  
Local Boundary ◽  
Lorentzian Signature ◽  
Special Cases ◽  
Non Local ◽  
Non Local Equations

Abstract Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking’s paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the quantum extremal islands of an evaporating black hole exist only in Lorentzian signature. Furthermore, the Euclidean equations for the Schwarzian mode are non-local, so it is unclear how to connect to the local, Lorentzian dynamics of an evaporating black hole. We address these issues with Schwinger-Keldysh techniques and show how the non-local equations reduce to the local ‘boundary particle’ description in special cases.

scholarly journals Asymptotic Stability of Nonlinear Discrete Fractional Pantograph Equations with Non-Local Initial Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 473
Author(s):  
Jehad Alzabut ◽  
A. George Maria Selvam ◽  
Rami Ahmad El-Nabulsi ◽  
D. Vignesh ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Current Collector ◽  
Stability Of Solutions ◽  
Electric Bus ◽  
Pantograph Equation ◽  
Non Local

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Δ*β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii’s and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

Reexamining the tropical Atlantic influence on ENSO using perfect model predictability experiments

2021 ◽  
Author(s):  
Ingo Richter ◽  
Yu Kosaka ◽  
Hiroki Tokinaga ◽  
Shoichiro Kido
Keyword(s):  
Initial Conditions ◽  
Boreal Summer ◽  
Similar Amount ◽  
Tropical Atlantic ◽  
Equatorial Atlantic ◽  
Boreal Spring ◽  
Modes Of Variability ◽  
Control Simulation ◽  
Starting Point ◽  
Perfect Model

&lt;p&gt;The potential influence of the tropical Atlantic on the development of ENSO has received increased attention over recent years. In particular equatorial Atlantic variability (also known as the Atlantic zonal mode or AZM) has been shown to be anticorrelated with ENSO, i.e. cold AZM events in boreal summer (JJA) tend to be followed by El Ni&amp;#241;o in winter (DJF), and vice versa for warm AZM events. One problem with disentangling the two-way interaction between the equatorial Atlantic and Pacific is that both ENSO and the AZM tend to develop in boreal spring (MAM).&lt;/p&gt;&lt;p&gt;Here we use a set of GCM sensitivity experiments to quantify the strength of the Atlantic-Pacific link. The starting point is a 1000-year free-running control simulation with the GFDL CM 2.1 model. From this control simulation, we pick years in which a cold AZM event in JJA is followed by an El Ni&amp;#241;o in DJF. These years serve as initial conditions for &amp;#8220;perfect model&amp;#8221; prediction experiments with 10 ensemble members each. In the control experiments, the predictions evolve freely for 12 months from January 1 of each selected year. In the second set of predictions, SSTs are gradually relaxed to climatology in the tropical Atlantic, so that the cold AZM event is suppressed. In the third set of predictions, we restore the tropical Pacific SSTs to climatology, so that the El Ni&amp;#241;o event is suppressed.&lt;/p&gt;&lt;p&gt;The results suggest that, on average, the tropical Atlantic SST anomalies increase the strength of El Ni&amp;#241;o in the following winter by about 10-20%. If, on the other hand, El Ni&amp;#241;o development is suppressed, the amplitude of the cold AZM event also reduces by a similar amount. The results suggest that, in the context of this GCM, the influence of AZM events on ENSO development is relatively weak but not negligible. The fact that ENSO also influences the AZM in boreal spring highlights the complex two-way interaction between these two modes of variability.&lt;/p&gt;

scholarly journals Chimera states and the interplay between initial conditions and non-local coupling

2017 ◽  
Vol 27 (3) ◽  
pp. 033110 ◽  
Author(s):  
Peter Kalle ◽  
Jakub Sawicki ◽  
Anna Zakharova ◽  
Eckehard Schöll
Keyword(s):  
Initial Conditions ◽  
Chimera States ◽  
Non Local ◽  
Local Coupling

Burgers' equation by non-local shot noise data

1994 ◽  
Vol 31 (A) ◽  
pp. 351-362 ◽  
Author(s):  
Donatas Surgailis ◽  
Wojbor A. Woyczynski
Keyword(s):  
Shot Noise ◽  
Random Fields ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Scaling Limit ◽  
Linear Partial Differential Equation ◽  
Local Case ◽  
Non Linear ◽  
Noise Data ◽  
Non Local

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).

Sensitivity Analysis and Inverse Problems in Microscale Heat Transfer

2015 ◽  
Vol 362 ◽  
pp. 209-223 ◽  
Author(s):  
Ewa Majchrzak ◽  
Jolanta Dziatkiewicz ◽  
Łukasz Turchan
Keyword(s):  
Heat Transfer ◽  
Sensitivity Analysis ◽  
Inverse Problems ◽  
Initial Conditions ◽  
Short Pulse ◽  
Relaxation Times ◽  
Coupling Factor ◽  
Hyperbolic Model ◽  
Short Pulse Laser ◽  
Microscale Heat Transfer

In the paper the selected problems related to the modeling of microscale heat transfer are presented. In particular, thermal processes occurring in thin metal films exposed to short-pulse laser are described by two-temperature hyperbolic model supplemented by appropriate boundary and initial conditions. Sensitivity analysis of electrons and phonons temperatures with respect to the microscopic parameters is discussed and also the inverse problems connected with the identification of relaxation times and coupling factor are presented. In the final part of the paper the examples of computations are shown.

scholarly journals Analytical-Numerical Calculation Algorithm of Algebraic Equations Roots with Specified Limits of Errors

2019 ◽  
Vol 18 (6) ◽  
pp. 1491-1514
Author(s):  
Yuri Bychkov ◽  
Elena Solovyeva ◽  
Sergei Scherbakov
Keyword(s):  
Numerical Method ◽  
Algebraic Equation ◽  
Initial Conditions ◽  
Absolute Error ◽  
Variable Order ◽  
Algebraic Equations ◽  
Adaptive Procedure ◽  
Calculation Algorithm ◽  
Mathematical Basis ◽  
Calculation Step

This paper proposes an algorithm for calculating approximate values of  roots of algebraic equations with a specified limit of absolute errors. A mathematical basis of the algorithm is an analytical-numerical method of solving nonlinear integral-differential equations with non-stationary coefficients. The analytical-numerical method belongs to the class of one-step continuous methods of variable order with an adaptive procedure for choosing a calculation step, a formalized estimate of the error of the performed calculations at each step and the error accumulated during the calculation. The proposed algorithm for calculating the approximate values of the roots of an algebraic equation with specified limit absolute errors consists of two stages. The results of the first stage are numerical intervals containing the unknown exact values of the roots of the algebraic equation. At the second stage, the approximate values of these roots with the specified limit absolute errors are calculated. As an example of the use of the proposed algorithm, defining the roots of the fifth-order algebraic equation with three different values of the limiting absolute error is presented. The obtained results allow drawing the following conclusions. The proposed algorithm enables to select numeric intervals that contain unknown exact values of the roots. Knowledge of these intervals facilitates the calculation of the approximate root values under any specified limiting absolute error. The algorithm efficiency, i.e., the guarantee of achieving the goal, does not depend on the choice of initial conditions. The algorithm is not iterative, so the number of calculation steps required for extracting a numerical interval containing an unknown exact value of any root of an algebraic equation is always restricted. The algorithm of determining a certain root of the algebraic equation is computationally completely autonomous.

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