Mathematical treatment of environmental models

Large-scale environmental models can successfully be used in different important for the modern society studies as, for example, in the investigation of the influence of the future climatic changes on pollution levels in different countries. Such models are normally described mathematically by non-linear systems of par- tial differential equations, which are defined on very large spatial domains and have to be solved numerically on very long time intervals. Moreover, very often many different scenarios have also to be developed and used in the investigations. There- fore, both the storage requirements and the computational work are enormous. The great difficulties can be overcome only if the following four tasks are successfully resolved: (a) fast and sufficiently accurate numerical methods are to be selected, (b) reliable and efficient splitting procedures are to be applied, (c) the cache memories of the available computers are to be efficiently exploited and (d) the codes are to be parallelized

Photon emission in a constant magnetic field in 2+1 dimensional space-time

We calculate by the proper-time method the amplitude of the two-photon emission by a charged fermion in a constant magnetic field in (2+1)-dimensional space-time. The relevant dynamics reduces to that of a supesymmetric quantum-mechanical system with one bosonic and one fermionic degrees of freedom.Comment: 18 pages. v2: references added, some significant changes in the introductio

PARALLEL COMPUTATIONS WITH LARGE-SCALE AIR\ud POLLUTION MODELS

Large-scale mathematical models are very powerful tools in the efforts to provide more\ud information and more detailed information about the pollution levels, especially about pollution\ud levels which exceed certain critical values.. However, the model used must satisfy at\ud least two conditions: (i) it must be verified that the model results are reliable and (ii) it\ud should be possible to carry out different study by using the model. It is clear that comprehensive\ud studies about relationships between different input parameters and the model results\ud can only be carried out (a) if the numerical methods used in the model are sufficiently\ud fast and (b) if the code runs efficiently on the available high-speed computers.\ud Some results obtained recently by a new unified version of the Danish Eulerian Model will\ud be presented in this paper

Solving advection equations by applying the crank-nicolson scheme combined with the richardson extrapolation

Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples. Copyright Zahari Zlatev et al

Parallel Computations with Large-scale Air Pollution Models

Large-scale mathematical models are very powerful tools in the efforts to provide more information and more detailed information about the pollution levels, especially about pollution levels which exceed certain critical values.. However, the model used must satisfy at least two conditions: (i) it must be verified that the model results are reliable and (ii) it should be possible to carry out different study by using the model. It is clear that comprehensive studies about relationships between different input parameters and the model results can only be carried out (a) if the numerical methods used in the model are sufficiently fast and (b) if the code runs efficiently on the available high-speed computers. Some results obtained recently by a new unified version of the Danish Eulerian Model will be presented in this paper.Великомасштабні математичні моделі – дуже потужний інструмент для одержання більш детальної інформації щодо рівнів забруднень. Проте використовувана модель повинна задовольнити принаймні двом умовам: (i) результати моделювання повинні бути надійними і (ii) повинна існувати можливість уточнення і вивчення різноманітних характеристик моделей. Всебічне вивчення відношень між різноманітними параметрами входу і результатами моделювання може бути виконане, якщо (a) чисельні методи, використовувані в моделі, достатньо швидкі та (b) програмне забезпечення на доступних швидкодіючих комп'ютерах достатньо ефективне. Подані результати рівнобіжної реалізації моделювання забруднення атмосфери, отримані в новій об'єднаній версії датської Ейлерової моделі.Крупномасштабные математические модели – очень мощный инструмент для получения более детальной информации относительно уровней загрязнений. Однако модель должна удовлетво- рить по крайней мере двум условиям: (i) результаты моделирования должны быть надежными и (ii) должна существовать возможность уточнения и изучения характеристик модели. Всестороннее изучение отношений между различными параметрами входа и результатами моделирования может быть выполнено, если (a) численные методы, используемые в модели, достаточно быстры и (b) программное обеспечение на доступных быстродействующих компь- ютерах достаточно эффективно. Представлены результаты параллельной реализации моделирования загрязнения атмосферы, полученные в новой объединенной версии датской Эйлеровой модели

A New Cosmological Model of Quintessence and Dark Matter

We propose a new class of quintessence models in which late times oscillations of a scalar field give rise to an effective equation of state which can be negative and hence drive the observed acceleration of the universe. Our ansatz provides a unified picture of quintessence and a new form of dark matter we call "Frustrated Cold Dark Matter" (FCDM). FCDM inhibits gravitational clustering on small scales and could provide a natural resolution to the core density problem for disc galaxy halos. Since the quintessence field rolls towards a small value, constraints on slow-roll quintessence models are safely circumvented in our model.Comment: Revised. Important new results added in response to referees comment

Cosmological Tracking Solutions

A substantial fraction of the energy density of the universe may consist of quintessence in the form of a slowly-rolling scalar field. Since the energy density of the scalar field generally decreases more slowly than the matter energy density, it appears that the ratio of the two densities must be set to a special, infinitesimal value in the early universe in order to have the two densities nearly coincide today. Recently, we introduced the notion of tracker fields to avoid this initial conditions problem. In the paper, we address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And, can tracker solutions explain why quintessence is becoming important today rather than during the early universe

The Revival of the Unified Dark Energy-Dark Matter Model ?

We consider the generalized Chaplygin gas (GCG) proposal for unification of dark energy and dark matter and show that it admits an unique decomposition into dark energy and dark matter components once phantom-like dark energy is excluded. Within this framework, we study structure formation and show that difficulties associated to unphysical oscillations or blow-up in the matter power spectrum can be circumvented. Furthermore, we show that the dominance of dark energy is related to the time when energy density fluctuations start deviating from the linear $\delta \sim a$ behaviour.Comment: 6 pages, 4 eps figures, Revtex4 style. New References are added. Some typos are corrected. Conclusions remain the sam