scholarly journals A theoretical study of a possible model of paramagnetic alums at low temperatures

1940 ◽  
Vol 176 (965) ◽  
pp. 203-213 ◽  
Keyword(s):  
Magnetic Field ◽  
Low Temperatures ◽  
Theoretical Study ◽  
Spontaneous Magnetization ◽  
Critical Value ◽  
Transition Curve ◽  
Thin Specimen ◽  
First Order ◽  
Freely Suspended ◽  
Line Of Critical Points

An attempt is made to examine theoretically the properties of paramagnetic alums at low temperatures. The model taken is a lattice of freely suspended magnets, all interactions except purely magnetic being neglected. Even with this simplification it is impossible at present to make rigorous calculations of the partition function, either on classical or quantum lines. A simple model is proposed, which is really a generalization of the Bragg - Williams theory enabling one to take account of the effect of a magnetic field. The few configurations whose energies are known are used to fix arbitrary constants in the expression assumed for the energy. The theory predicts that the state of lowest energy is either a spontaneously magnetized, state for a long thin specimen, or a state in which alternate rows of magnets point in opposite directions for a sphere, spontaneous magnetization appearing in an ellipsoid with an eccentricity greater than a certain critical value. The transition curve bounding the region in which the antiparallel state is stable consists partly of a line of Curie points corresponding to transitions of the second, order, passing smoothly into a line of critical points corresponding to a transition of the first order. The effect of shape on the magnetic properties of the specimen seems to be experimentally verified, but the rough nature of the theory prevents it being more than qualitative.

Experimental and Theoretical Study on Magnetoelastic Buckling of a Ferromagnetic Cantilevered Beam-Plate

1978 ◽  
Vol 45 (2) ◽  
pp. 355-360 ◽  
Author(s):  
K. Miya ◽  
K. Hara ◽  
K. Someya
Keyword(s):  
Magnetic Field ◽  
Theoretical Study ◽  
Critical Value ◽  
The Finite Element Method ◽  
Wide Face ◽  
Field Distortion ◽  
Cantilevered Beam ◽  
Magnetically Soft Material ◽  
Experimental Values ◽  
The Magnetic Field

When a cantilever of magnetically soft material is inserted with its wide face normal to a uniform magnetic field and the magnetic field is increased to a critical value the cantilever will buckle. The experimental magnetoelastic buckling fields and the theoretical ones differ by a factor of two. A magnetic field distortion near an edge of the specimen is here evaluated based on the finite-element method and the results are applied to the experimental results so as to explain the discrepancy between the experiment and the theory. The corrected experimental values are within 15 percent of the theoretical values. The effect of demagnetization on the buckling field is here demonstrated as well as the effect of specimen dimensions.

scholarly journals EFFECT OF STRONG MAGNETIC FIELD ON THE FIRST-ORDER ELECTROWEAK PHASE TRANSITION

1999 ◽  
Vol 14 (06) ◽  
pp. 407-415 ◽  
Author(s):  
R. FIORE ◽  
A. TIESI ◽  
L. MASPERI ◽  
A. MÉGEVAND
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Higgs Mass ◽  
Critical Value ◽  
Broken Symmetry ◽  
Electroweak Phase Transition ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
The Magnetic Field

The broken-symmetry electroweak vacuum is destabilized in the presence of a magnetic field stronger than a critical value. Such magnetic field may be generated in the phase transition and restore the symmetry inside the bubbles. A numerical calculation indicates that the first-order phase transition is delayed but may be completed for a sufficient low value of the Higgs mass unless the magnetic field is extremely high.

scholarly journals Tricriticality of the Blume–Emery–Griffiths model in thin films of stacked triangular lattices

2016 ◽  
Vol 30 (07) ◽  
pp. 1650071
Author(s):  
Sahbi El Hog ◽  
H. T. Diep
Keyword(s):  
Exchange Interaction ◽  
Low Temperatures ◽  
Lattice Site ◽  
Film Surface ◽  
Critical Value ◽  
Layer By Layer ◽  
Superfluid Phase ◽  
First Order ◽  
Interior Layers ◽  
Triangular Lattices

We study in this paper the Blume–Emery–Griffiths model in a thin film of stacked triangular lattices. The model is described by three parameters: bilinear exchange interaction between spins [Formula: see text], quadratic exchange interaction [Formula: see text] and single-ion anisotropy [Formula: see text]. The spin [Formula: see text] at the lattice site [Formula: see text] takes three values [Formula: see text]. This model can describe the mixing phase of He-4 [Formula: see text] and He-3 [Formula: see text] at low temperatures. Using Monte Carlo simulations, we show that there exists a critical value of [Formula: see text] below (above) which the transition is of second-(first-)order. In general, the temperature dependence of the concentrations of He-3 is different from layer by layer. At a finite temperature in the superfluid phase, the film surface shows a deficit of He-4 with respect to interior layers. However, effects of surface interaction parameters can reverse this situation. Effects of the film thickness on physical properties will be also shown as functions of temperature.

MAGNETIC FIELD DEPENDENT RELAXATION TIME IN p-InSb AT LOW TEMPERATURES

1981 ◽  
Vol 42 (C5) ◽  
pp. C5-689-C5-693
Author(s):  
J. D.N. Cheeke ◽  
G. Madore ◽  
A. Hikata
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Low Temperatures ◽  
Field Dependent

Simple Systems

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Magnetic Field ◽  
Low Temperatures ◽  
General Framework ◽  
Gibbs State ◽  
Macroscopic System ◽  
Basic Model ◽  
System A ◽  
Paramagnetic Salt ◽  
High And Low Temperatures ◽  
Simple Systems

Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic oscillator, a rotor, and a spin in a magnetic field. These applications serve to illustrate how a key function associated with the Gibbs state, the so-called partition function, is calculated in practice, how the entropy function is obtained via a Legendre transformation, and how such systems behave in the limits of high and low temperatures. After discussing these simple systems, this chapter considers a first example where multiple constituents are assembled into a macroscopic system: a basic model of a paramagnetic salt. It also investigates the size of energy fluctuations and how—in the case of the paramagnet—these fluctuations scale with the number of constituents.

scholarly journals Figures of merit for stellarators near the magnetic axis

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Matt Landreman
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Axis ◽  
Configuration Design ◽  
New Paradigm ◽  
First Order ◽  
Figures Of Merit ◽  
Minor Radius ◽  
Error Field ◽  
Quantities Of Interest

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.

scholarly journals Review of Multi-Physics Modeling on the Active Magnetic Regenerative Refrigeration

2021 ◽  
Vol 26 (2) ◽  
pp. 47
Author(s):  
Julien Eustache ◽  
Antony Plait ◽  
Frédéric Dubas ◽  
Raynal Glises
Keyword(s):  
Magnetic Field ◽  
Low Temperatures ◽  
Room Temperature ◽  
State Of The Art ◽  
Vapor Compression ◽  
Crucial Step ◽  
Potential Alternative ◽  
Vapor Compression Refrigeration ◽  
Preliminary Study ◽  
Physics Modeling

Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic regenerative refrigeration (AMRR) cycles. Initially, this effect was widely used for cryogenic applications to achieve very low temperatures. However, this technology must be improved to replace vapor-compression devices operating around room temperature. Therefore, over the last 30 years, a lot of studies have been done to obtain more efficient devices. Thus, the modeling is a crucial step to perform a preliminary study and optimization. In this paper, after a large introduction on MCE research, a state-of-the-art of multi-physics modeling on the AMRR cycle modeling is made. To end this paper, a suggestion of innovative and advanced modeling solutions to study magnetocaloric regenerator is described.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

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