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Magnetic properties of a classical XY spin dimer in a planar magnetic field
No full textSingle-molecule magnetism originates from the strong intra-molecular magnetic coupling of a small number of interacting spins. Such spins generally interact very weakly with the neighboring spins in the other molecules of the compound, therefore, inter-molecular spin couplings are negligible. In certain cases the number of magnetically coupled spins is as small as a dimer, a system that can be considered the smallest nanomagnet capable of storing non-trivial magnetic information on the molecular level. Additional interesting patterns arise if the spin motion is confined to a two-dimensional space. In such a scenario, clusters consisting of spins with large-spin values are particularly attractive since their magnetic interactions can be described well in terms of classical Heisenberg XY spins. In this work we calculate exactly the magnetic properties of a nanomagnetic dimer of classical XY spins in a planar external magnetic field. The problem is solved by employing a mathematical approach whose idea is the introduction of auxiliary spin variables into the starting expression of the partition function. Results for the total internal energy, total magnetic moment, spin-spin correlation function and zero-field magnetic susceptibility can serve as a basis to understand the magnetic properties of large-spin dimer building blocks
Empirical validation of Radiance-IES daylight simulation for furnished and unfurnished rooms under a tropical sky
No full textNowadays, many researchers – especially engineers and architects – apply daylighting simulation tools during the building design process to investigate daylighting performance for a range of purposes. However, International Commission on Illumination (CIE, from the French name of the organisation, Commission Internationale de l’Eclairage) sky models are considered for many such simulation tools. The characteristics of tropical sky are different from those of CIE skies, hence the usage and validity of these tools could be unreliable for research involving tropical regions. The aim of this study is to validate the Radiance program in the Integrated Environmental Solution – Virtual Environment (IES-VE) software by measuring daylight in furnished and unfurnished rooms under Malaysian tropical sky. Daylighting measurement and simulation were carried out over eight days in unfurnished and furnished rooms under both intermediate and overcast skies. The case room was drawn by ModelIT and the related furniture was modelled by the Component program in IES-VE 2014. The mean difference between the measured and simulated results in the furnished and unfurnished rooms showed that the daylight factor (DF) and daylight ratio (DR) are more accurate than the work plane illuminance (WPI) and external illuminance. The study highlights furniture as a significant internal element that can effectively reduce the light levels in a room. It is concluded that the Radiance-IES relative ratios DF and DR are validated for use in furnished and unfurnished rooms under tropical skies
Oct 8th, 2016 - Prairie View A&M vs Alabama Hornets
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Matching Transversal Edge Domination in Graphs
Get PDFLet G =(V,E) be a graph. A subset X of E is called an edge dominating set of G if every edge in E - X is adjacent to some edge in X . An edge dominating set which intersects every maximum matching inG is called matching transversal edge dominating set. The minimum cardinality of a matching transversal edge dominating set is called the matching transversal edge domination number of G and is denoted by γmt(G). In this paper, we begin an investigation of this parameter
Non Markovian Queue with Two Types service Optional Re-service and General Vacation Distribution
Get PDFWe consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with probability 1 -θ: The re-service periods and vacation periods are assumed to be general. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived and thus we deduce the steady state results. We obtain the average queue size and average waiting time. Some system performance measures and numerical illustrations are discussed
On Arresting the Complex Growth Rates in Rotatory Triply Diffusive Convection
Get PDFLinear stability of a triply diffusive fluid layer (one of the components may be heat) has been mathematically analyzed in the presence of uniform vertical rotation. Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation of growing amplitude are derived which are important especially when at least one of the boundaries is rigid so that exact solutions in closed form are not obtainable. Further, it is proved that the results obtained herein are uniformly valid for any combination of dynamically free and rigid boundaries. It is also shown that the existing results of rotatory hydrodynamic Rayleigh Benard convection and rotatory hydrodynamic double diffusive convection follow as a consequence
Hydromagnetic peristaltic transportation with porous medium through an asymmetric vertical tapered channel and joule heating
Get PDFThe present paper deals with a theoretical investigation of the hydromagnetic peristaltic transportation with porous medium through coaxial asymmetric vertical tapered channel and joule heating which has been studied under the assumption of long wavelength approximations. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, temperature and heat transfer coefficient at both walls were calculated. The effects of various emerging parameters, Hartmann number, Non-uniform parameter, Prandtl number, Heat generator parameter, Brinkman number, Porous parameter are discussed through the use of graphs. We notice from the figures that the temperature of the fluid increases in the entire vertical tapered channel with an increase in Magnetic field, Brinkman number, Prandtl number and Heat generation parameter. We notice that the temperature profiles are found almost parabolic in nature. Further, it can be noticed that the heat transfer coefficient gradually decreases and then increases with increasing values of the Hartmann number, Brinkman number, Prandtl number, and Heat generation parameter in the entire vertical tapered channel at the right wall. It can be seen that the heat transfer coefficient slowly decreases and then increases in the rest of the channel with increasing values of the Hartmann number, Brinkman number, Prandtl number, and Heat generation parameter in entire vertical tapered channel at left the wall. It can be observed that the coefficient of heat transfer gives the oscillatory behaviour which is due to the propagation of peristaltic waves
On the Exchange Property for the Mehler-Fock Transform
Get PDFThe theory of Schwartz Distributions opened up a new area of mathematical research, which in turn has provided an impetus in the development of a number of mathematical disciplines, such as ordinary and partial differential equations, operational calculus, transformation theory and functional analysis. The integral transforms and generalized functions have also shown equivalent association of Boehmians and the integral transforms. The theory of Boehmians, which is a generalization of Schwartz distributions are discussed in this paper. Further, exchange property is defined to construct Mehler-Fock transform of tempered Boehmians. We investigate exchange property for the Mehler-Fock transform by using the theory of Mehler-Fock transform of distributions. Algebraic properties and convergence is also proved for this relation on the tempered Boehmians which is a natural extension of tempered distribution
On the Slow Growth and Approximation of Entire Function Solutions of Second-Order Elliptic Partial Differential Equations on Caratheodory Domains
Get PDFIn this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far