47,159 research outputs found
Integrable Magnetic Model of Two Chains Coupled by Four-Body Interactions
An exact solution for an XXZ chain with four-body interactions is obtained
and its phase diagram is determined. The model can be reduced to two chains
coupled by four-body interactions, and it is shown that the ground state of the
two-chain model is magnetized in part. Furthermore, a twisted four-body
correlation function of the anti-ferromagnetic Heisenberg chain is obtained.Comment: 7 pages, LaTeX, to be published in J. Phys. Soc. Jpn., rederived the
mode
The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field
A nonlinear susceptibilities (the third derivative of a magnetization
by a magnetic field ) of the =1/2 ferromagnetic Heisenberg chain and the
classical Heisenberg chain are calculated at low temperatures In both
chains the nonlinear susceptibilities diverge as and a linear
susceptibilities diverge as The arbitrary spin Heisenberg
ferromagnet has a scaling relation between and
The scaling function
=(2/3)-(44/135) + O() is common to all values of spin
Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques
Galilei covariance and (4,1) de Sitter space
A vector space G is introduced such that the Galilei transformations are
considered linear mappings in this manifold. The covariant structure of the
Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988) 63; 36 (1988) 83) is
derived and the tensor analysis is developed. It is shown that the Euclidean
space is embedded the (4,1) de Sitter space through in G. This is an
interesting and useful aspect, in particular, for the analysis carried out for
the Lie algebra of the generators of linear transformations in G.Comment: Late
Transient Response Dynamic Module Modifications to Include Static and Kinetic Friction Effects
A methodology that supports forced transient response dynamic solutions when both static and kinetic friction effects are included in a structural system model is described. Modifications that support this type of nonlinear transient response solution are summarized for the transient response dynamics (TRD) NASTRAN module. An overview of specific modifications for the NASTRAN processing subroutines, INITL, TRD1C, and TRD1D, are described with further details regarding inspection of nonlinear input definitions to define the type of nonlinear solution required, along with additional initialization requirements and specific calculation subroutines to successfully solve the transient response problem. The extension of the basic NASTRAN nonlinear methodology is presented through several stages of development to the point where constraint equations and residual flexibility effects are introduced into the finite difference Newmark-Beta recurrsion formulas. Particular emphasis is placed on cost effective solutions for large finite element models such as the Space Shuttle with friction degrees of freedom between the orbiter and payloads mounted in the cargo bay. An alteration to the dynamic finite difference equations of motion is discussed, which allows one to include friction effects at reasonable cost for large structural systems such as the Space Shuttle. Data are presented to indicate the possible impact of transient friction loads to the payload designer for the Space Shuttle. Transient response solution data are also included, which compare solutions without friction forces and those with friction forces for payloads mounted in the Space Shuttle cargo bay. These data indicate that payload components can be sensitive to friction induced loads
Optimum design of magnetic field environment for axonal growth control in nerve cell regeneration process using electromagnetic field analyses
In this study, an optimum magnetic field environment for the nerve axonal extension and control of axonal growth direction in the nerve cell generation process was searched by using electromagnetic finite element analyses. Recently, the developments of 3D-scaffold structures employing biodegradable polymers have been an attracting attention for the clinical treatments of damaged nerve tissues. The magnetic stimulation is introduced to accelerate the regeneration speed of nerve axon inside the 3D-scaffold. According to experimental observation of Blackman, C.F. and his research group (1993) [1], it was found that 50 Hz AC magnetic field has promoted the regeneration of axonal extension in the case of pheochromocytoma cells (PC12). They identified the optimum configuration of the coil and the threshold value of driving current for the initiation of PC12 axon growth. However, they did not evaluate analytically the magnetic flux density and the magnetic field in the cell culture liquid for the PC12 axon growth initiation. Therefore, at first we employed the electromagnetic finite element analyses (FEA) to evaluate the magnetic flux density in the case of Blackman’s experiment. Simultaneously, we identified the relative magnetic permeability of Dulbecco’s Modified Eagle Medium (DMEM) as 1.01 at 50 Hz. Finally, we obtained the value of magnetic flux density inside DMEM as 4.2 T. Next, we try to design the configuration of Helmholtz coil, which can generate an optimum magnetic field to stimulate most effectively for PC12 axon extension. It is confirmed that the magnetic field gradient affect the extensional speed of PC12 axon, which can be achieved by setup the one peripheral coil and two coils at the center. We found an optimum configuration of Helmholtz coil to generate the magnetic field environment and fabricate an experimental bioreactor for PC12 cell culture. We examined the effectiveness of magnetic stimulation for PC12 nerve axon’s extension quantitatively. Further, we try to find the relationship between the magnetic field gradient and the direction of nerve axon’s extension
Unstable geodesics and topological field theory
A topological field theory is used to study the cohomology of mapping space.
The cohomology is identified with the BRST cohomology realizing the physical
Hilbert space and the coboundary operator given by the calculations of
tunneling between the perturbative vacua. Our method is illustrated by a simple
example.Comment: 28 pages, OCU-15
Quantum Spin Chains and Riemann Zeta Function with Odd Arguments
Riemann zeta function is an important object of number theory. It was also
used for description of disordered systems in statistical mechanics. We show
that Riemann zeta function is also useful for the description of integrable
model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a
probability of formation of a ferromagnetic string in the anti-ferromagnetic
ground state in thermodynamics limit. We prove that for short strings the
probability can be expressed in terms of Riemann zeta function with odd
arguments.Comment: LaTeX, 7 page
Modified Spin Wave Analysis of Low Temperature Properties of Spin-1/2 Frustrated Ferromagnetic Ladder
Low temperature properties of the spin-1/2 frustrated ladder with
ferromagnetic rungs and legs, and two different antiferromagnetic next nearest
neighbor interaction are investigated using the modified spin wave
approximation in the region with ferromagnetic ground state. The temperature
dependence of the magnetic susceptibility and magnetic structure factors is
calculated. The results are consistent with the numerical exact diagonalization
results in the intermediate temperature range. Below this temperature range,
the finite size effect is significant in the numerical diagonalization results,
while the modified spin wave approximation gives more reliable results. The low
temperature properties near the limit of the stability of the ferromagnetic
ground state are also discussed.Comment: 9 pages, 8 figure
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