Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

Thermodynamic Analysis of Ethanol Dry Reforming: Effect of Combined Parameters

The prospect of ethanol dry reforming process to utilize CO2 for conversion to hydrogen, syngas, and carbon nanofilaments using abundantly available biofuel—ethanol, and widely available environmental pollutant CO2 is very enthusiastic. A thermodynamic analysis of ethanol CO2 reforming process is done using Gibbs free energy minimization methodology within the temperature range 300–900°C, 1–10 bar pressure, and CO2 to carbon (in ethanol) ratio (CCER) 1–5. The effect of individual as well as combined effect of process parameters such as temperature, pressure, and CCER was determined on the product distribution. Optimum process conditions for maximising desired products and minimizing undesired products for applications such as gas to liquids (GTL) via fischer tropsch synthesis, syngas generation for Solid oxide fuel cells, and carbon nanofilament manufacture were found in this study.

Application of COSMO-RS Method for the Prediction of Liquid-Liquid Equilibrium of Water/n-Dodecane/1-Butanol

The liquid-liquid equilibrium (LLE) for the system water-dodecane-butanol was estimated using the UNIQUAC model. In the UNIQUAC model interaction parameters were estimated from the vapor-liquid equilibrium (VLE) and LLE data of their constituent binary pairs. The water-dodecane-butanol LLE was experimentally measured at 298.15 K. Phase stability constraints were taken into account while calculating the binary interaction parameters from the mutual solubility data. The COSMO-RS method was used to estimate the activity coefficient in the miscible binary pair. The ternary LLE composition was predicted using the experimental VLE data as well as using the COSMO-RS calculated activity coefficient data along with the experimental mutual solubility data. In the latter case the root mean square deviation (RMSD) for the distribution of butanol between aqueous and organic phase is 0.24%. The corresponding UNIFAC model prediction is 7.63%.

Thermodynamic and Interfacial Properties of DTABr/CTABr Mixed Surfactant Systems in Ethanolamine/Water Mixtures: A Conductometry Study

Mixed-micelle formation in the binary mixtures of dodecyltrimethylammonium bromide (DTABr) and cetyltrimethylammonium bromide (CTABr) surfactants in water-ethanolamine mixed solvent systems has been studied by conductometric method in the temperature range of 298.1 to 313.1 K at 5 K intervals. It was observed that the presence of ethanolamine forced the formation of mixed micelle to lower total surfactant concentration than in water only. The synergistic interaction was quantitatively investigated using the theoretical models of Clint and Rubingh. The interaction parameter β12 was negative at all the mole fractions of DTABr in the surfactant mixtures indicating a strong synergistic interaction, with the presence of ethanolamine in the solvent system resulting in a more enhanced synergism in micelle formation than in water only. The free energy of micellization ΔGM values was more negative in water-ethanolamine mixed solvent system than in pure water indicating more spontaneity in mixed micelle formation in the presence of ethanolamine than in pure water.

Thermodynamical Analysis of the Flow and Heat Transfer over a Static and a Moving Wedge

The first and second law characteristics of fluid flow and heat transfer over a static and a moving wedge are investigated. With the help of suitable similarity transformations, the governing boundary layer equations for the velocity and temperature fields are transformed into ordinary differential equations and are solved numerically. The velocity and the temperature profiles are obtained for various parameters and are utilized to compute the entropy generation number Ns and the Bejan number Be. The effects of various physical parameters on the entropy generation number and the Bejan number are depicted through graphs and are discussed qualitatively. It is observed that the entropy production rate is less in case of wedge moving in the opposite direction to flow as compared to static wedge.

Wavelength Width Dependence of Cavity Temperature Distribution in Semiconductor Diode Laser

The study of heat distribution in laser diode shows that there is nonuniform temperature distribution in cavity length of laser diode. In this paper, we investigate the temperature difference in laser diode cavity length and its effect on laser bar output wavelength width that mounted on usual CS model. In this survey at the first, laser was simulated then the simulations result was compared with experimental test result. The result shows that for each emitter there is difference, about 2.5 degree between the beginning and end of cavity.

A Derivation of the Main Relations of Nonequilibrium Thermodynamics

The principles of nonequilibrium thermodynamics are discussed, using the concept of internal variables that describe deviations of a thermodynamic system from the equilibrium state. While considering the first law of thermodynamics, work of internal variables is taken into account. It is shown that the requirement that the thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. These statements, in line with the axioms introducing internal variables can be considered as basic principles of nonequilibrium thermodynamics. While considering stationary nonequilibrium situations close to equilibrium, it is shown that known linear parities between thermodynamic forces and fluxes and also the production of entropy, as a sum of products of thermodynamic forces and fluxes, are consequences of fundamental principles of thermodynamics.

Analytical Solution of Nonlinear Boundary Value Problem for Fin Efficiency of Convective Straight Fins with Temperature-Dependent Thermal Conductivity

We have employed homotopy analysis method (HAM) to evaluate the approximate analytical solution of the nonlinear equation arising in the convective straight fins with temperature-dependent thermal conductivity problem. Solutions are presented for the dimensionless temperature distribution and fin efficiency of the nonlinear equation. The analytical results are compared with previous work and satisfactory agreement is noted.

Perturbation Solution for Radiating Viscoelastic Fluid Flow and Heat Transfer with Convective Boundary Condition in Nonuniform Channel with Hall Current and Chemical Reaction

A mathematical analysis has been performed for heat and mass transfer of a time-dependent MHD flow of an electrically conducting viscoelastic fluid in nonuniform vertical channel with convective boundary condition. The fluid flow is considered between a vertical long wavy wall and a parallel flat wall saturated with the porous medium. The effects of thermal radiation, heat absorption, chemical reaction, and Hall current are taken into account. The prevailing nonlinear partial differential equations are derived by considering Boussinesq approximation, and the same equations are solved analytically using perturbation technique. Further the expressions for skin friction, Nusselt number, and Sherwood number are presented. The effects of various pertinent parameters on different flow fields are analyzed graphically and tabularly. It is found that effects of Hall parameter and Biot number are unfavorable on velocity profiles, but this trend is reverse for the effect of thermal and solutal Grashof numbers. The expressions of different flow fields satisfy the imposed boundary conditions, which is shown in all graphs; this implies accuracy of the solution.

Analytical Solution of MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet with Partial Slip

This paper investigates the hydromagnetic boundary layer flow and heat transfer of a non-Newtonian Casson fluid in the neighborhood of a stagnation point over a stretching surface in the presence of velocity and thermal slips at the boundary. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformations. The analytic solutions are developed by a homotopy analysis method (HAM). The results pertaining to the present study indicate that the flow and temperature fields are significantly influenced by Casson parameter (), the magnetic parameter , the velocity slip parameter , and the thermal slip parameter . An increase in the velocity slip parameter causes decrease in the flow velocity, while an increase in the value of the thermal slip parameter causes increase in the temperature of the fluid. It is also observed that the velocity at a point decreases with increase in .