Thermodynamics of Bidisperse Ferrofluids in Zero External Magnetic Field: Theory and Simulations

2015 ◽  
Vol 233-234 ◽  
pp. 331-334
Author(s):  
Anna Yu. Solovyova ◽  
Ekaterina A. Elfimova
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Free Energy ◽  
External Magnetic Field ◽  
Volume Concentration ◽  
Helmholtz Free Energy ◽  
Hard Spheres ◽  
Particle Volume ◽  
Simulation Data ◽  
Theoretical Predictions

The thermodynamic properties of a ferrofluid modeled by a bidisperse system of dipolar hard spheres in the absence of external magnetic field are investigated using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy in terms of particle volume concentration. Comparison between the theoretical predictions and simulation data shows a great agreement of the results.

A NONPERTURBATIVE CALCULATION FOR THE EFFECTIVE POTENTIAL OF THE $\left(\frac{g}{4}\phi^{4}-J\phi\right)_{1+1}$ SCALAR FIELD THEORY USING THE OSCILLATOR REPRESENTATION METHOD WITH BOREL RESUMMATION

2007 ◽  
Vol 22 (06) ◽  
pp. 1265-1278
Author(s):  
ABOUZEID M. SHALABY ◽  
S. T. EL-BASYOUNY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Phase Transition ◽  
Scalar Field ◽  
External Magnetic Field ◽  
Effective Potential ◽  
Oscillator Representation ◽  
Constructive Field Theory ◽  
Representation Method ◽  
Oscillator Representation Method

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

2016 ◽  
Vol 791 ◽  
pp. 237-259
Author(s):  
Krzysztof A. Mizerski ◽  
Eligiusz Wajnryb
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Effective Viscosity ◽  
Hard Spheres ◽  
Magnetic Interactions ◽  
Point Dipole ◽  
Basic Principles ◽  
Self Diffusion ◽  
Viscosity Coefficients ◽  
Short Time

The virial corrections to short-time self- and collective diffusion coefficients as well as the effective viscosity are calculated for suspensions of hard spheres with the same radii and constant (blocked within the particle) magnetization modelled by a point dipole. Analytic, integral formulae derived from basic principles of statistical mechanics are provided for both cases – in the absence and in the presence of an external magnetic field. In the former case the diffusion and viscosity coefficients are evaluated numerically as a function of the strength of magnetic interactions between the particles and it is reported that the translational collective diffusion coefficient is significantly greater than all the other coefficients. In the presence of an external magnetic field the coefficients become anisotropic and are evaluated in the asymptotic regime of weak interparticle magnetic interactions.

Equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field

1972 ◽  
Vol 7 (3) ◽  
pp. 445-459 ◽  
Author(s):  
J. R. Kan
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
External Magnetic Field ◽  
Constant Field ◽  
Current Component ◽  
Equilibrium Solutions ◽  
Plasma Parameters ◽  
Equilibrium Configurations ◽  
Field Aligned Current ◽  
A Current

A class of equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field is presented. The present slab model contains the diamagnetic current jy, and the field-aligned current jz for arbitrary βc (= particle pressure/magnetic pressure of the applied constant field). For fixed βc and field-aligned current, our model admits a family of equilibrium solutions in which the diamagnetic currents range from zero to a maximum value. The amount of diamagnetic current flowing in a machine depends on the width of the machine, the field-aligned current and other plasma parameters. The Helmholtz free energy of the system is calculated under the constraints that the total number of particles and the field-aligned current are conserved. The least unstable equilibrium configuration in a machine is obtained by minimizing the free energy under the stated constraints among all equilibria whose plasma widths do not exceed the width of the machine.

LARGE DEVIATIONS AND THE RANDOM ENERGY MODEL

2001 ◽  
Vol 15 (01) ◽  
pp. 1-15 ◽  
Author(s):  
T. C. DORLAS ◽  
J. R. WEDAGEDERA
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
External Magnetic Field ◽  
Large Deviation ◽  
Error Correcting Codes ◽  
Energy Model ◽  
Random Energy Model ◽  
Recent Letter ◽  
Random Energy ◽  
Deviation Property

We present a simple proof of the formula for the free energy of the random energy model using a large deviation property which holds almost surely with respect to the randomness. This proof is extended to the case with external magnetic field leading to the solution of a model with higher-order ferromagnetic term. It is shown that this model is useful for Sourlas' application to error-correcting codes as was already pointed out in a recent letter by the authors.

scholarly journals Excitation of electrostatic ion-cyclotron-like modes by the electron density ripple in dusty magnetoplasmas

2009 ◽  
Vol 75 (4) ◽  
pp. 433-436
Author(s):  
P. K. SHUKLA
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
External Magnetic Field ◽  
Electron Density ◽  
Mathieu Equation ◽  
Ion Cyclotron ◽  
Unstable Solutions

AbstractIt is shown that electrostatic ion-cyclotron (EIC)-like modes can be excited by the pre-existing electron density ripple across the external magnetic field in a dusty magnetoplasma. For this purpose, we use the ion continuity and momentum equations, together with the Boltzmann-distributed electrons, and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that the EIC-like modes in dusty magnetoplasmas can be driven due to the free energy in the electron density ripple.

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