Phase Transition of Meshwork Models for Spherical Membranes

We have studied two types of meshwork models by using the canonical Monte Carlo simulation technique. The first meshwork model has elastic junctions, which are composed of vertices, bonds, and triangles, while the second model has rigid junctions, which are hexagonal (or pentagonal) rigid plates. Two-dimensional elasticity is assumed only at the elastic junctions in the first model, and no two-dimensional bending elasticity is assumed in the second model. Both of the meshworks are of spherical topology. We find that both models undergo a first-order collapsing transition between the smooth spherical phase and the collapsed phase. The Hausdorff dimension of the smooth phase is H≃2 in both models as expected. It is also found that H≃2 in the collapsed phase of the second model, and that H is relatively larger than 2 in the collapsed phase of the first model, but it remains in the physical bound, i.e., H<3. Moreover, the first model undergoes a discontinuous surface fluctuations transition at the same transition point as that of the collapsing transition, while the second model undergoes a continuous transition of surface fluctuation. This indicates that the phase structure of the meshwork model is weakly dependent on the elasticity at the junctions. This work was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.     

Phase structure of a spherical surface model on fixed connectivity meshes

An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The shape of surfaces is maintained by a one-dimensional bending energy, which is defined on the mesh, and no two-dimensional bending energy is included in the Hamiltonian.     

Shape transformation transitions in a model of fixed-connectivity surfaces supported by skeletons

A compartmentalized surface model of Nambu and Goto is studied on triangulated spherical surfaces by using the canonical Monte Carlo simulation technique. One-dimensional bending energy is defined on the skeletons and at the junctions, and the mechanical strength of the surface is supplied by the one-dimensional bending energy defined on the skeletons and junctions. The compartment size is characterized by the total number L^′ of bonds between the two-neighboring junctions and is assumed to have values in the range from L^′ = 2 to L^′ = 8 in the simulations, while that of the previously reported model is characterized by L^′ = 1, where all vertices of the triangulated surface are the junctions. Therefore, the model in this paper is considered to be an extension of the previous model in the sense that the previous model is obtained from the model in this paper in the limit of L^′↦1. The model in this paper is identical to the Nambu-Goto surface model without curvature energies in the limit of L^′↦∞ and hence is expected to be ill-defined at sufficiently large L^′. One remarkable result obtained in this paper is that the model has a well-defined smooth phase even at relatively large L^′ just as the previous model of L^′↦ 1. It is also remarkable that the fluctuations of surface in the smooth phase are crucially dependent on L^′; we can see no surface fluctuation when L^′≤ 2, while relatively large fluctuations are seen when L^′≥ 3.     

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

We numerically study the phase structure of two types of triangulated spherical surface models, which includes an in-plane shear energy in the Hamiltonian, and we found that the phase structure of the models is considerably influenced by the presence of the in-plane shear elasticity. The models undergo a first-order collapsing transition and a first-order (or second-order) transition of surface fluctuations; the latter transition was reported to be of second-order in the first model without the in-plane shear energy. This leads us to conclude that the in-plane elasticity strengthens the transition of surface fluctuations. We also found that the in-plane elasticity decreases the variety of phases in the second model without the in-plane energy. The Hamiltonian of the first model is given by a linear combination of the Gaussian bond potential, a one-dimensional bending energy, and the in-plane shear energy. The second model is obtained from the first model by replacing the Gaussian bond potential with the Nambu-Goto potential, which is defined by the summation over the area of triangles.     

Phase transition of compartmentalized surface models

Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation transition. The first model is a fluid surface one. The vertices can freely diffuse only inside the compartments, and they are prohibited from the free diffusion over the surface due to the domain boundaries. The second is a skeleton model. The surface shape of the skeleton model is maintained only by the domain boundaries, which are linear chains with rigid junctions. Therefore, we can conclude that the first-order transitions occur independent of whether the shape of surface is mechanically maintained by the skeleton (=the domain boundary) or by the surface itself.     

Structural instability in high-T c superconducting oxides

Two broad internal friction (attenuation as well) peaks in YBCO measured at around 120 K and 250 K are found to exhibit the characteristics of a first-order phase transition. X-ray diffraction indicates no symmetry change on cooling from room temperature but only a downward jump of the lattice parameters was observed. This is referred to as a phase-like transition (PLT) and further confirmed by stress-strain, specific heat and Debye-Waller factor measurements. There always occurs a phase-like transition at 10-30 K above T _c in YBCO, BSCCO and TBCCO which disappears in the non-superconducting phases. Ultrasonic studies on single-crystal BSCCO reveal a pronounced elastic anisotropy in the c-plane and a velocity minimum associated with PLT. The overall trend of elastic stiffening below room temperature and some discrepancies and questions in elasticity measurements so far observed for high-T _c oxides have been explained or clarified in terms of an abnormal fast change of lattice parameters.     

A polymerization-depolymerization model for generation of contractile force during bacterial cell division

We have investigated the pressure-induced phase transition of NiO and other structural properties using three-body potential approach. NiO undergoes phase transition from B1 (rocksalt) to B2 (CsCl) structure associated with a sudden collapse in volume showing first-order phase transition. A theoretical study of high pressure phase transition and elastic behaviour in transition metal compounds using a three-body potential caused by the electron shell deformation of the overlapping ion was carried out. The phase transition pressure and other properties predicted by our model is closer to the phase transition pressure predicted by Eto et al.      

Quasi-2D and prewetting transitions of square-well fluids on a square-well substrate

Molecular simulation methodologies are employed to study the first-order transition of variable square-well (SW) fluids on a wide range of weak attractive surfaces. Surface phase diagram of SW fluids of attractive well diameter λ _ff = 1.5, 1.75, 2.0 on a smooth, structureless surface modelled by a SW potential is reported via grand-canonical transition-matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Fluids with λ _ff = 1.5 and 1.75 show quasi-2D vapour–liquid phase transition; on the other hand, prewetting transition is visible for a SW fluid with larger well-extent λ _ff = 2.0. The prewetting line, its length, and closeness to the bulk saturation curve are found to depend strongly on the nature of the fluid–fluid and fluid–wall interaction potentials. Boundary tension of surface coexistence films is calculated by two methods. First, the finite size scaling approach of Binder is used to evaluate the boundary tension via GC-TMMC. Second, the results of the boundary tension are verified by virtue of its relation to the pressure tensor components, which are calculated using a NVT-Monte Carlo approach. The results from the two methods are in good agreement. Boundary tension is found to increase with the increase in the wall–fluid interaction range for the quasi-2D system; conversely, boundary tension for thin–thick film, at prewetting transition, decreases with the increase in the wall–fluid interaction range.     

Dielectric studies of the phase transition in {N(CH3)4}2HgCl4

Dielectric properties of single-crystal {N(CH₃)₄}₂HgCl₄ (structure at room temperature; orthorhombic Pmcn) have been measured in a temperature range from 4 K to about 370 K. The dielectric constant along the a-, b-, and c-axes shows a break at 278 K. No other anomalies are detected in the temperature range studied. The transition temperature increases linearly with increasing hydrostatic pressure at a rate of 0.20 K/MPa. Twin boundaries are observed in the low-temperature phase on b-plate specimens. The results indicate that the phase transition in {N(CH₃)₄}₂HgCl₄ is ferroelastic, as in {N(CH₃)₄}₂XBr₄ (X: Mn, Co, Zn).     

Electronic properties and superconductivity of amorphous Si1-xAux alloys near the metal-insulator transition

We report on specific-heat and resistivity measurements on quench-condensed Si_1-xAu_x films for 0.11 ⩽ x 0.36 in the temperature range 0.35 K ⩽ T ⩽ 6 K. A distinct increase of the specificheat derived electronic density of states at the Fermi level is observed at x_b ≈ 0.2, i.e., in the vicinity of the metal-insulator transition occurring for our samples at x_c = 0.16. This suggests a different type of bonding between Au and Si for x < x_b and x > x_b. While resistive transitions to superconductivity are observed for x⩾0.21, the absence of a specific-heat anomaly at the transition points to filamentary superconductivity except for × = 0.35 where a sizable anomaly is seen. The difference in various electronic properties between differently prepared samples of these metastable alloys, in particular the influence of different preparation and annealing temperatures is emphasized. It is suggested that these differences are caused by incipient phase separation in the room-temperature prepared samples.     

Continuum theory of retroviral capsids

We present a self-assembly phase diagram for the shape of retroviral capsids, based on continuum elasticity theory. The spontaneous curvature of the capsid proteins drives a weakly first-order transition from spherical to spherocylindrical shapes. The conical capsid shape which characterizes the HIV-1 retrovirus is never stable under unconstrained energy minimization. Only under conditions of fixed volume and/or fixed spanning length can the conical shape be a minimum energy structure. Our results indicate that, unlike the capsids of small viruses, retrovirus capsids are not uniquely determined by the molecular structure of the constituent proteins but depend in an essential way on physical constraints present during assembly.     

Order-disorder transition in Na3Bi(PO4)2

Na₃Bi(PO₄)₂ exhibits several phase transitions at about 575, 820 and 905°C. The structure was determined at ambient temperature (α-form) and above the first transition (β-form). The α-form cell is monoclinic with a = 19.86(1), b = 5.353(6), c = 13.96(3) Å, β = 110.64(7)°, Z = 8, space group P2₁/ _c ; the structure was solved from 3769 independent reflections to an R value, calculated on intensities, of 0.069. The β-form cell is orthorhombic with a = 18.71(3), b = 7.18(2), c = 5.429(7) Å, Z = 4, space group Pnam; the structure was solved to an R value, calculated on structure factors, of 0.055 using intensities of 858 unique reflections measured on a single crystal at 650°C. Both structures are related to that of glaserite. At high temperature, one of the PO₄ tetrahedra is statistically disordered over two positions related by the m-mirror. Below the transition, ordering of this ion leads to a unit cell of lower symmetry. At the transition, two individuals grow on the two sides of the m-mirror which disappears; thus, at ambient temperature, the crystals are systematically twinned. Above the second transition, the unit cell is hexagonal.     

Effect of pre-existing baryon inhomogeneities on the dynamics of quark-hadron transition

Baryon number inhomogeneities may be generated during the epoch when the baryon asymmetry of the universe is produced, e.g. at the electroweak phase transition. These lumps will have a lower temperature than the background. Also the value ofT _c will be different in these regions. Since a first-order quark-hadron (Q–H) transition is susceptible to small changes in temperature, we investigate the effect of the presence of such baryonic lumps on the dynamics of the Q–H transition. We find that the phase transition is delayed in these lumps for significant overdensities. Consequently, we argue that baryon concentration in these regions grows by the end of the transition. We mention some models which may give rise to such high baryon overdensities before the Q–H transition.     

Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C_s/epsilon and C_b/epsilon where C_s and C_b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C_s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2–3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.     

Twin refinement below room temperature in the 1-2-3 highT c superconductors

Thea–b microtwinning in the 90 K superconductors of the Y(1)Ba(2)Cu(3)O(7–) family of perovscites is studied by transmission electron microscopy betwen 300 and 85 K. Thermally stable twin spacings of order 300 Å are observed in dense polycrystalline material. In grains with free surfaces of sufficiently regular shape, the twin pattern is observed to refine at low temperature, either spontaneously or by low temperature thermal cycling, from a spacing of about 1000 Å to about 300 Å. In grains with free surfaces of less regular shape, the twins can be brought to disappear at low temperature after a sufficient electron dosis, and to reappear reversibly. A correlation between transition temperature and twin spacing is discussed.     

Effects of the Mn/Co ratio on the magnetic transition and magnetocaloric properties of Mn1+xCo1-xGe alloys

We have investigated the magnetic transition and magnetocaloric effects of Mn 1+x Co 1 x Ge alloys by tuning the ratio of Mn/Co.With increasing Mn content,a series of first-order magnetostructural transitions from ferromagnetic to paramagnetic states with large changes of magnetization are observed at room temperature.Further increasing the content of Mn (x=0.11) gives rise to a single second-order magnetic transition.Interestingly,large low-field magnetic entropy changes with almost zero magnetic hysteresis are observed in these alloys.The effects of Mn/Co ratio on magnetic transition and magnetocaloric effects are discussed in this paper.     

Phase transitions in a fluid surface model with a deficit angle term

Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases; crumpled, branched-polymer, linear, and tubular. The linear phase and the tubular phase appear to be separated by a first-order transition. It is also found that there is no long-range two-dimensional order in the model. In fact, no smooth surface can be seen in the whole region of the curvature modulus α, which is the coefficient of the deficit angle term in the Hamiltonian. The bending energy, which is not included in the Hamiltonian, remains large even at sufficiently large α in the tubular phase. On the other hand, the surface is spontaneously compactified into a one-dimensional smooth curve in the linear phase; one of the two degrees of freedom shrinks, and the other degree of freedom remains along the curve. Moreover, we find that the rotational symmetry of the model is spontaneously broken in the tubular phase just as in the same model on the fixed connectivity surfaces.     

Folding transitions of the square-diagonal lattice

We address the problem of “phantom” folding of the tethered membrane modeled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities K₁ and K₂ for respectively long and short bonds, we derive the complete phase diagram of the model, using transfer matrix calculations. The latter displays two transition curves, one corresponding to a first-order (ferromagnetic) folding transition, and the other to a continuous (anti-ferromagnetic) unfolding transition.     

受限于圆柱体内半刚性高分子链的螺旋结构转变

采用非格点珠簧球链模型, 结合Monte Carlo方法, 研究了半刚性高分子链受限于无限长圆柱体的构象性质. 模拟结果表明: 在圆柱体内表面附近具有吸附能的情况下, 当弯曲能b由小到大变化时, 发现半刚性高分子链由开始时的无规则被吸附在圆柱体内表面, 到逐渐出现螺旋结构, 最后伸展成类似棒状的结构. 同时计算了不同弯曲能b时的半刚性高分子链的平均螺旋数N_t, 平均每条链单体的螺旋百分比P_h和能量涨落. 发现高分子链螺旋结构的形成与转变, 不仅与圆柱体半径R的大小有关, 还与弯曲能b的大小有关. 研究结果能有助于加深对受限生物大分子构象的认识.     

Influence of hydrogenation on the electronic structure and the itinerant-electron metamagnetic transition in strong magnetocaloric compound La(Fe0.88Si0.12)13

The influence of interstitial hydrogen on the electronic structure and the itinerant-electron metamagnetic (IEM) transition in strong magnetocaloric compound La(Fe_0.88Si_0.12)₁₃H_1.6 has been investigated by Mössbauer spectroscopy. A slight change in the average hyperfine field at 4.2 K was observed after hydrogen absorption. In contrast, the thermally induced first-order transition related to the IEM transition for y=1.6 appears at the Curie temperature T_C=330 K, much higher than T_C=195 K for y=0.0. The increase of isomer shift δ_IS at 4.2 K indicates that the valence electron transfer from hydrogen to Fe is negligibly small, hence the change in the magnetic state is closely associated with a volume expansion after hydrogen absorption. No change in shape by hydrogenation for the Mössbauer spectra in the paramagnetic state has been observed except for a difference in only δ_IS, indicating the volume expansion by hydrogenation is isotropic. Accordingly, the significant increase of T_C by hydrogen absorption is attributed to the magnetovolume effect associated with characteristic feature in IEM compounds. A discontinuous change of ferromagnetic moment, ΔM, around T_C has been observed by Mössbauer spectra, as expected from the magnetization measurement. The value of ΔM is slightly decreased by increase of T_C after hydrogenation but its magnitude is almost the same due to the stabilization of ferromagnetic moment. As a result, strong magnetocaloric effect is maintained up to room temperature after hydrogenation.