Reduced differential transform method for solving (1 + n) – Dimensional Burgers' equation

AbstractThis paper discusses a recently developed semi-analytic technique so called the reduced differential transform method (RDTM) for solving the (1 + n) – dimensional Burgers' equation. The method considers the use of the appropriate initial or boundary conditions and finds the solution without any discretization, transformation, or restrictive assumptions. Four numerical examples are provided in order to validate the efficiency and reliability of the method and furthermore to compare its computational effectiveness with other analytical methods available in the literature

New Travelling Wave Solutions of Two Nonlinear Physical Models by Using a Modified Tanh-Coth Method

In this work, a modified tanh – coth method is used to derive travelling wave solutions for (2 + 1)-dimensional Zakharov-Kuznetsov (ZK) equation and (3 + 1)-dimensional Burgers equation. A new variable is used to solve these equations and established new travelling wave solutions. </jats:p

Radiation from Violently Accelerated Bodies

A determination is made of the radiation emitted by a linearly uniformly accelerated uncharged dipole transmitter. It is found that, first of all, the radiation rate is given by the familiar Larmor formula, but it is augmented by an amount which becomes dominant for sufficiently high acceleration. For an accelerated dipole oscillator, the criterion is that the center of mass motion become relativistic within one oscillation period. The augmented formula and the measurements which it summarizes presuppose an expanding inertial observation frame. A static inertial reference frame will not do. Secondly, it is found that the radiation measured in the expanding inertial frame is received with 100% fidelity. There is no blueshift or redshift due to the accelerative motion of the transmitter. Finally, it is found that a pair of coherently radiating oscillators accelerating (into opposite directions) in their respective causally disjoint Rindler-coordinatized sectors produces an interference pattern in the expanding inertial frame. Like the pattern of a Young double slit interferometer, this Rindler interferometer pattern has a fringe spacing which is inversely proportional to the proper separation and the proper frequency of the accelerated sources. The interferometer, as well as the augmented Larmor formula, provide a unifying perspective. It joins adjacent Rindler-coordinatized neighborhoods into a single spacetime arena for scattering and radiation from accelerated bodies.Comment: 29 pages, 1 figure, Revte

Thermodynamic relations in a driven lattice gas: numerical exprements

We explore thermodynamic relations in non-equilibrium steady states with numerical experiments on a driven lattice gas. After operationally defining the pressure and chemical potential in the driven lattice gas, we confirm numerically the validity of the integrability condition (the Maxwell relation) for the two quantities whose values differ from those for an equilibrium system. This implies that a free energy function can be constructed for the non-equilibrium steady state that we consider. We also investigate a fluctuation relation associated with this free energy function. Our result suggests that the compressibility can be expressed in terms of density fluctuations even in non-equilibrium steady states.Comment: 4 pages, 4 figure

Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

Grids of Stellar Models and Frequencies with CLES + LOSC

We present a grid of stellar models, obtained with the CLES evolution code, following the specification of ESTA-Task1, and the corresponfing seismic properties, computed with the LOSC code. We provide a complete description of the corresponding files that will be available on the ESTA web-pages.Comment: 8 pages, accepted for publication in Astrophys. Space Sci. (CoRoT/ESTA Volume

Kinks in the Hartree approximation

The topological defects of the lambda phi^4 theory, kink and antikink, are studied in the Hartree approximation. This allows us to discuss quantum effects on the defects in both stationary and dynamical systems. The kink mass is calculated for a number of parameters, and compared to classical, one loop and Monte Carlo results known from the literature. We discuss the thermalization of the system after a kink antikink collision. A classical result, the existence of a critical speed, is rederived and shown for the first time in the quantum theory. We also use kink antikink collisions as a very simple toy model for heavy ion collisions and discuss the differences and similarities, for example in the pressure. Finally, using the Hartree Ensemble Approximation allows us to study kink antikink nucleation starting from a thermal (Bose Einstein) distribution. In general our results indicate that on a qualitative level there are few differences with the classical results, but on a quantitative level there are some import ones.Comment: 20 pages REVTeX 4, 17 Figures. Uses amsmath.sty and subfigure.sty. Final version, fixed typo in published versio

Infectious diseases co-morbidities among patients attending Kogi State University Teaching Hospital: a ten-year retrospective study

Background: Co-existence of more than one acute or chronic infectious diseases in a person either concurrently or sequentially with consequent economic burden varies differently from one part of the world to another, with regional and population specific patterns. This study aims to provide co-morbid patho-epidemiological pattern of six infectious diseases; HIV, tuberculosis (TB), malaria, syphilis, hepatitis B and hepatitis C virus infections. Methodology: This research is a ten-year retrospective review of records of patients admitted at various wards of Kogi State University Teaching hospital and referred to the Laboratory Department of the hospital for investigations between June 2012 and July 2021. HIV was screened using the national serial algorithm, TB was diagnosed with the GeneXpert MTB, malaria parasite was identified by blood film microscopy, and syphilis, hepatitis B and hepatitis C viruses were screened using rapid diagnostic kits. Data were analysed with SPSS version 23.0 and association of variables with respect to gender and age group was determined using Chi square, with p&lt; 0.05 considered to be statistically significant. Results: A total of 223 patients were retrospectively reviewed with 102 (45.7%) males and 121 (54.3%) females. Co-morbidities occurred most frequently among age groups 21-30 years (34.1%), 31-40 years (39.0%) and 41-50 years (16.6%). The most frequent co-morbidity pattern was HIV/TB (81.6%) followed by HBV/MP (4.5%), HIV/HBV (4.0%), HIV/MP (3.1%), TB/MP (2.7%), HBV/HCV (2.2%) while HCV/MP, TB/HCV, HCV/syphilis, and TB/HBV were (0.4%) each. There was no significant difference in the frequency of co-morbidity with respect to gender and age groups of patients (p&gt;0.05). Conclusion: Co-existence of chronic infectious disease in a person increases the risk of morbidities and mortalities. Therefore, diagnosis, and concurrent treatment and management of co-morbid infectious diseases should be incorporated into our routine healthcare system and appropriate resources should be allotted for this in health plans. &nbsp; Frebch title: Co-morbidités des maladies infectieuses chez les patients fréquentant l'hôpital universitaire de l'État de Kogi: une étude rétrospective sur dix ans Contexte: La coexistence de plusieurs maladies infectieuses aiguës ou chroniques chez une personne, simultanément ou séquentiellement, avec un fardeau économique conséquent, varie différemment d'une partie du monde à l'autre, avec des schémas régionaux et spécifiques à la population. Cette étude vise à fournir le schéma patho-épidémiologique comorbide de six maladies infectieuses; VIH, tuberculose (TB), paludisme, syphilis, infections par le virus de l'hépatite B et de l'hépatite C. Méthodologie: Cette recherche est un examen rétrospectif sur dix ans des dossiers de patients admis dans divers services de l'hôpital universitaire de l'État de Kogi et référés au département de laboratoire de l'hôpital pour des enquêtes entre juin 2012 et juillet 2021. Le VIH a été dépisté à l'aide de la série nationale algorithme, la tuberculose a été diagnostiquée avec le GeneXpert MTB, le parasite du paludisme a été identifié par microscopie de frottis sanguin et les virus de la syphilis, de l'hépatite B et de l'hépatite C ont été dépistés à l'aide de kits de diagnostic rapide. Les données ont été analysées avec SPSS version 23.0 et l'association des variables par rapport au sexe et au groupe d'âge a été déterminée à l'aide du Chi carré, avec p&lt;0,05 considéré comme statistiquement significatif. Résultats: Un total de 223 patients ont été revus rétrospectivement avec 102 (45,7%) hommes et 121 (54,3%) femmes. Les comorbidités sont survenues le plus fréquemment dans les groupes d'âge 21-30 ans (34,1 %), 31-40 ans (39,0%) et 41-50 ans (16,6%). Le schéma de comorbidité le plus fréquent était le VIH/TB (81,6%), suivi du VHB/MP (4,5%), du VIH/VHB (4,0%), du VIH/MP (3,1%), de la TB/MP (2,7%), du VHB/VHC (2,2%) tandis que VHC/MP, TB/VHC, VHC/syphilis et TB/VHB étaient (0,4%) chacun. Il n'y avait pas de différence significative dans la fréquence des comorbidités en fonction du sexe et des tranches d'âge des patients (p&gt;0,05). Conclusion: La coexistence de maladies infectieuses chroniques chez une personne augmente le risque de morbidité et de mortalité. Par conséquent, le diagnostic, le traitement et la gestion concomitants des maladies infectieuses comorbides doivent être intégrés à notre système de soins de santé de routine et des ressources appropriées doivent être allouées à cet effet dans les plans de santé

Quantum spin systems at positive temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\beta$ and the magnitude of the quantum spins \CalS satisfy \beta\ll\sqrt\CalS. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with \CalS\gg1. The most notable examples are the quantum orbital-compass model on $\Z^2$ and the quantum 120-degree model on $\Z^3$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.Comment: 47 pages, version to appear in CMP (style files included

Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes

Rindler's acceleration-induced partitioning of spacetime leads to a nature-given interferometer. It accomodates quantum mechanical and wave mechanical processes in spacetime which in (Euclidean) optics correspond to wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting, reflection, and interference. These processes are described in terms of amplitudes which behave smoothly across the event horizons of all four Rindler sectors. In this context there arises quite naturally a complete set of orthonormal wave packet histories, one of whose key properties is their "explosivity index". In the limit of low index values the wave packets trace out fuzzy world lines. By contrast, in the asymptotic limit of high index values, there are no world lines, not even fuzzy ones. Instead, the wave packet histories are those of entities with non-trivial internal collapse and explosion dynamics. Their details are described by the wave processes in the above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit interference process. These wave processes are applied to elucidate the amplification of waves in an accelerated inhomogeneous dielectric. Also discussed are the properties and relationships among the transition amplitudes of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version of the figures and of related papers available at http://www.math.ohio-state.edu/~gerlac