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

BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry

The quantization of spontaneously broken gauge theories in noncommutative geometry(NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang and Ne'eman recently succeeded in realizing the BRST quantization of gauge theories in NCG in the matrix derivative approach proposed by Coquereaux et al. The present author has proposed a characteristic formulation to reconstruct a gauge theory in NCG on the discrete space $M_4\times Z_{_N}$. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST invariant Lagrangian in the same way as Lee, Hwang and Ne'eman and apply it to the SU(2)$\times$U(1) gauge theory.Comment: RevTeX, page

Anisotropy on the Fermi Surface of the Two-Dimensional Hubbard Model

We investigate anisotropic charge fluctuations in the two-dimensional Hubbard model at half filling. By the quantum Monte Carlo method, we calculate a momentum-resolved charge compressibility $\kappa (\bm{k}) = {d < n(\bm{k}) >}/{d \mu}$, which shows effects of an infinitesimal doping. At the temperature $T \sim {t^2}/{U}$, $\kappa (\bm{k})$ shows peak structure at the $(\pm \pi/2,\pm \pi/2)$ points along the $|k_x| + |k_y| = \pi$ line. A similar peak structure is reproduced in the mean-filed calculation for the d-wave pairing state or the staggered flux state.Comment: 5 pages, 3 figures, figures and presentation are modifie

Mott Transition in the Two-Dimensional Flux Phase

Effects of the electron-electron interaction in the two-dimensional flux phase are investigated. We treat the half-filled Hubbard model with a magnetic flux $\pi$ per plaquette by the quantum Monte Carlo method. When the interaction is small, an antiferromagnetic long-range does not exist and the charge fluctuation is different from that of the Mott insulator It suggests that the Mott transition occurs at finite strength of the interaction in the flux phase, which is in contrast to the standard Hubbard model.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Novel vortex lattice transition in d-wave superconductors

We study the vortex state in a magnetic field parallel to the $c$ axis in the framework of the extended Ginzburg Landau equation. We find the vortex acquires a fourfold modulation proportional to $\cos(4\phi)$ where $\phi$ is the angle ${\bf r}$ makes with the $a$-axis. This term gives rise to an attractive interaction between two vortices when they are aligned parallel to $(1,1,0)$ or $(1,-1,0)$. We predict the first order vortex lattice transition at $B=H_{cr}\sim \kappa^{-1} H_{c2}(t)$ from triangular into the square lattice tilted by $45^\circ$ from the $a$ axis. This gives the critical field $H_{cr}$ a few Tesla for YBCO and Bi2212 monocrystals at low temperatures ($T\leq 10 K$).Comment: 6 pages, 4 figure

Numerical Replica Limit for the Density Correlation of the Random Dirac Fermion

The zero mode wave function of a massless Dirac fermion in the presence of a random gauge field is studied. The density correlation function is calculated numerically and found to exhibit power law in the weak randomness with the disorder dependent exponent. It deviates from the power law and the disorder dependence becomes frozen in the strong randomness. A classical statistical system is employed through the replica trick to interpret the results and the direct evaluation of the replica limit is demonstrated numerically. The analytic expression of the correlation function and the free energy are also discussed with the replica symmetry breaking and the Liouville field theory.Comment: 5 pages, 4 figures, REVTe

A Homological Approach to Belief Propagation and Bethe Approximations

We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This definition reveals a set of conserved quantities under Belief Propagation and gives new insight on the relationship of its equilibria with the critical points of Bethe free energy.Comment: 14 pages, submitted for the 2019 Geometric Science of Information colloquiu

Collapse of Charge Gap in Random Mott Insulators

Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte-Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase transition due to randomness is observed associated with the collapse of the charge ordering. We also treat random Hubbard model focusing on the Mott gap. Although the randomness closes the Mott gap and low-lying states are created, which is observed in the charge compressibility, no (quasi-) Fermi surface singularity is formed. It implies localized nature of the low-lying states.Comment: RevTeX with 3 postscript figure