In-plane deformation of a triangulated surface model with metric degrees of freedom

Using the canonical Monte Carlo simulation technique, we study a Regge calculus model on triangulated spherical surfaces. The discrete model is statistical mechanically defined with the variables $X$, $g$ and $\rho$, which denote the surface position in ${\bf R}^3$, the metric on a two-dimensional surface $M$ and the surface density of $M$, respectively. The metric $g$ is defined only by using the deficit angle of the triangles in {$M$}. This is in sharp contrast to the conventional Regge calculus model, where {$g$} depends only on the edge length of the triangles. We find that the discrete model in this paper undergoes a phase transition between the smooth spherical phase at $b to infty$ and the crumpled phase at $b to 0$, where $b$ is the bending rigidity. The transition is of first-order and identified with the one observed in the conventional model without the variables $g$ and $\rho$. This implies that the shape transformation transition is not influenced by the metric degrees of freedom. It is also found that the model undergoes a continuous transition of in-plane deformation. This continuous transition is reflected in almost discontinuous changes of the surface area of $M$ and that of $X(M)$, where the surface area of $M$ is conjugate to the density variable $\rho$.Comment: 13 pages, 7 figure

Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

Skyrmions in chiral magnetic materials are topologically stable and energetically balanced spin configurations appearing under the presence of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI). Much of the current interest has focused on the effects of magneto-elastic coupling on these interactions under mechanical stimuli, such as uniaxial stresses for future applications in spintronics devices. Recent studies suggest that skyrmion shape deformations in thin films are attributed to an anisotropy in the coefficient of DMI, such that $D_{x}\!\not=\!D_{y}$, which makes the ratio $\lambda/D$ anistropic, where the coefficient of FMI $\lambda$ is isotropic. It is also possible that $\lambda_{x}\!\not=\!\lambda_{y}$ while $D$ is isotropic for $\lambda/D$ to be anisotropic. In this paper, we study this problem using a new modeling technique constructed based on Finsler geometry (FG). Two possible FG models are examined: In the first (second) model, the FG modeling prescription is applied to the FMI (DMI) Hamiltonian. We find that these two different FG models' results are consistent with the reported experimental data for skyrmion deformation. We also study responses of helical spin orders under lattice deformations corresponding to uniaxial extension/compression and find a clear difference between these two models in the stripe phase, elucidating which interaction of FMI and DMI is deformed to be anisotropic by uniaxial stresses.Comment: 42 pages, 23 figure

Monte Carlo studies of skyrmion stabilization under geometric confinement and uniaxial strain

Geometric confinement (GC) of skyrmions in nanodomains plays a crucial role in skyrmion stabilization. This confinement effect decreases the magnetic field necessary for skyrmion formation and is closely related to the applied mechanical stresses. However, the mechanism of GC is unclear and remains controversial. Here, we numerically study the effect of GC on skyrmion stabilization and find that zero Dzyaloshinskii-Moriya interaction (DMI) coupling constants imposed on the boundary surfaces of small thin plates cause confinement effects, stabilizing skyrmions in the low-field region. Moreover, the confined skyrmions are further stabilized by tensile strains parallel to the plate, and the skyrmion phase extends to the low-temperature region. This stabilization occurs due to the bulk anisotropic DMI coupling constant caused by lattice deformations. Our simulation data are qualitatively consistent with reported experimental data on skyrmion stabilization induced by tensile strains applied to a thin plate of the chiral magnet ${\rm Cu_2OSeO_3}$.Comment: 33 pages, 16 figure

Finsler geometry modeling of reverse piezoelectric effect in PVDF

We apply the Finsler geometry (FG) modeling technique to study the electric field-induced strain in ferroelectric polymers. Polyvinylidene difluoride (PVDF) has a negative longitudinal piezoelectric coefficient, which is unusual in ferroelectrics, and therefore the shape changes in this material are hard to predict. We find that the results of Monte Carlo simulations for the FG model are in good agreement with experimental strain-electric field curves of PVDF-based polymers in both longitudinal and transverse directions. This implies that FG modeling is suitable for reproducing the reverse piezoelectric effect in PVDF

Calcium Channel Blockers, More than Diuretics, Enhance Vascular Protective Effects of Angiotensin Receptor Blockers in Salt-Loaded Hypertensive Rats

The combination therapy of an angiotensin receptor blocker (ARB) with a calcium channel blocker (CCB) or with a diuretic is favorably recommended for the treatment of hypertension. However, the difference between these two combination therapies is unclear. The present work was undertaken to examine the possible difference between the two combination therapies in vascular protection. Salt-loaded stroke-prone spontaneously hypertensive rats (SHRSP) were divided into 6 groups, and they were orally administered (1) vehicle, (2) olmesartan, an ARB, (3) azelnidipine, a CCB, (4) hydrochlorothiazide, a diuretic, (5) olmesartan combined with azelnidipine, or (6) olmesartan combined with hydrochlorothiazide. Olmesartan combined with either azelnidipine or hydrochlorothiazide ameliorated vascular endothelial dysfunction and remodeling in SHRSP more than did monotherapy with either agent. However, despite a comparable blood pressure lowering effect between the two treatments, azelnidipine enhanced the amelioration of vascular endothelial dysfunction and remodeling by olmesartan to a greater extent than did hydrochlorothiazide in salt-loaded SHRSP. The increased enhancement by azelnidipine of olmesartan-induced vascular protection than by hydrochlorothiazide was associated with a greater amelioration of vascular nicotinamide adenine dinucleotide phosphate (NADPH) oxidase activation, superoxide, mitogen-activated protein kinase activation, and with a greater activation of the Akt/endothelial nitric oxide synthase (eNOS) pathway. These results provided the first evidence that a CCB potentiates the vascular protective effects of an ARB in salt-sensitive hypertension, compared with a diuretic, and provided a novel rationale explaining the benefit of the combination therapy with an ARB and a CCB