Relaxation Height in Energy Landscapes: An Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We prove sufficient conditions to identify multiple metastable states. Since this analysis typically involves non-trivial technical issues, we give different conditions that can be chosen appropriately depending on the specific model under study. We show how these results can be used to attack the problem of multiple metastable states via the use of the modern approaches to metastability. We finally apply these general results to the Blume–Capel model for a particular choice of the parameters for which the model happens to have two multiple not degenerate in energy metastable states. We estimate in probability the time for the transition from the metastable states to the stable state. Moreover we identify the set of critical configurations that represent the minimal gate for the transition.     

Numerical Simulation of Electromagnetic Waves Scattering by Discrete Exterior Calculus

We show how to construct discrete Maxwell equations by discrete exterior calculus. The new scheme has many virtues compared to the traditional Yee＇s scheme： it is a multisymplectic scheme and keeps geometric properties. Moreover, it can be applied on triangular mesh and thus is more adaptive to handle domains with irregular shapes. We have implemented this scheme on a Java platform successfully and our experimental results show that this scheme works well.     

Selecting the shape of supported metal nanocrystals: Pd huts, hexagons, or pyramids on SrTiO3(001)

Increasing interest in oxide supported nanoparticle science and technology is stimulating research into controlling nanocrystal shape. Pd forms nanocrystals on the surface of SrTiO3(001), and depending on the crystallographic interface of the Pd with the substrate three shapes can be created: truncated pyramids, huts, and hexagonal shaped disks. Scanning tunneling microscopy reveals that the nanocrystal shapes are determined by the substrate reconstruction and the substrate temperature during deposition. A thermodynamic model is used to show that the pyramids and huts are stable structures, and that the hexagons are trapped in a metastable state.     

Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the Miller-Robert-Sommeria (MRS) entropy under these sole constraints. We assume that these constraints are selected by properties of forcing and dissipation. We find that the vorticity fluctuations are Gaussian while the mean flow is characterized by a linear [`(w)]-y\overline{\omega}-\psi relationship. Furthermore, we prove that the maximization of entropy at fixed energy, circulation and microscopic enstrophy is equivalent to the minimization of macroscopic enstrophy at fixed energy and circulation. This provides a justification of the minimum enstrophy principle from statistical mechanics when only the microscopic enstrophy is conserved among the infinite class of Casimir constraints. Relaxation equations towards the statistical equilibrium state are derived. These equations can serve as numerical algorithms to determine maximum entropy or minimum enstrophy states. We use these relaxation equations to study geometry induced phase transitions in rectangular domains. In particular, we illustrate with the relaxation equations the transition between monopoles and dipoles predicted by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)]. We take into account stable as well as metastable states and show that metastable states are robust and have negative specific heats. This is the first evidence of negative specific heats in that context. We also argue that saddle points of entropy can be long-lived and play a role in the dynamics because the system may not spontaneously generate the perturbations that destabilize them.     

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.     

Shapes of lipid monolayer domains: Solutions using elliptic functions

Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative line tension and a positive curvature energy at the boundary, and a corresponding shape equation was derived by the variation of the approximated domain energy (Phys. Rev. Lett. 93, 206101 (2004)). Here we further incorporate surface pressure into the shape equation and show that the equation can be analytically solved: the curvature of the domain boundary is exactly obtained as an elliptic function of arc-length. We find that a circular domain can grow into bean-and peach-like domains with pressure, i.e., dipping and cuspidal transitions of circle by compression. The comparison with the experimental observation shows nice agreement.     

Reorientation,multidomain states and domain walls in diluted magnetic semiconductors

The competition between surface/interface and intrinsic anisotropies yields a number of specific reorientation effects and strongly influences magnetization processes in diluted magnetic semiconductors as (Ga,Mn)As and (In,Mn)As. We develop a phenomenological theory to describe reorientation transitions and the accompanying multidomain states applicable to layers of these magnetic semiconductors. It is shown that the magnetic phase diagrams of such systems include a region of four-phase domain structure with four adjoining areas of two-phase domains as well as several regions with coexisting metastable states. We demonstrate that the parameters of isolated domain walls in (Ga,Mn)As nanolayers are extremely sensitive to applied magnetic field and can vary in a broad range. This can be used in microdevices of magnetic semiconductors with pinned domain walls. For (Ga,Mn)As epilayers with perpendicular anisotropy the geometrical parameters of domains have been calculated.     

Lattice-supported surface solitons in nonlocal nonlinear media

We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on the domains of existence and stability of the surface solitons, focusing on new types of dipole solitons residing partially inside the optical lattice. We find that such solitons feature strongly asymmetric shapes and that they are stable in large parts of their existence domain.     

Spin-polarized zero-energy states in BN/C core–shell quantum dots

Boron-nitride (BN) domains in graphene or graphene domains in BN monolayer offer additional freedoms for tuning the electronic properties of these BN/C nanostructures, which is quite crucial for the applications in nanoscale devices. Based on first-principles calculations combined with a simple Hubbard model, we show that the electron zero-energy states (ZESs) of BN/graphene core–shell quantum dots (QDs) in triangular shapes can be well tuned by varying the size and topology of each domain. The net spin of the systems is dominated by the graphene segment which can be described by a Lieb?s theorem. We also demonstrated that a π-electron Hubbard model within a mean-field approximation is implementable in dealing with the electron spin-polarization of BN/C hetero-structured graphene-like materials. This provides an efficient theoretical approach for the BN/C systems where electron spin-polarization is involved.     

Emergent rotational symmetries in disordered magnetic domain patterns

Uniaxial systems often form labyrinthine domains that exhibit short-range order but are macroscopically isotropic and would not be expected to exhibit precise symmetries. However, their underlying frustration results in a multitude of metastable configurations of comparable energy, and driving such a system externally might lead to pattern formation. We find that soft x-ray speckle diffraction patterns of the labyrinthine domains in CoPd/IrMn heterostructures reveal a diverse array of hidden rotational symmetries about the magnetization axis, thereby suggesting an unusual form of emergent order in an otherwise disordered system. These symmetries depend on applied magnetic field, magnetization history, and scattering wave vector. Maps of rotational symmetry exhibit intriguing structures that can be controlled by manipulating the applied magnetic field in concert with the exchange bias condition.     

Strong attraction between charged spheres due to metastable ionized states

We report a mechanism which can lead to long-range attractions between like-charged spherical macroions, stemming from the existence of metastable ionized states. We show that the ground state of a single highly charged colloid plus a few excess counterions is overcharged. For the case of two highly charged macroions in their neutralizing divalent counterion solution we demonstrate that, in the regime of strong Coulomb coupling, the counterion clouds are very likely to be unevenly distributed, leading to one overcharged and one undercharged macroion. This long-living metastable configuration in turn leads to a long-range Coulomb attraction.     

Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.     

Photoluminescence decay and time-resolved spectroscopy of cubic yttria-stabilized zirconia

The time-resolved spectra and luminescence decays of cubic yttria-stabilized zirconia single crystals were investigated in the 100–300 K temperature range. At each temperature the time-resolved spectra are dominated by a yellow-orange broad band with a shoulder in the green region, and their shapes appear similar to those displayed in fluorescence. In addition, the shapes remain almost independent of the delay times over the range between 0.04 and 0.4 ms after excitation. The luminescence decays can be satisfactorily described by the superposition of two exponential functions, as well as by two expressions commonly given for decays related to disorder. In the three cases, the temperature dependences of the time constants and the other parameters derived from these expressions are analyzed. The time constants can be accounted for by assuming a radiative decay from two metastable levels with a typical separation of 0.057±0.005 eV. Some correlations between the parameters from the luminescence-decay formulae are given. The results are in good agreement with luminescence due to radiative recombinations at donor F-type levels in which complexes formed by oxygen vacancies in a disordered sublattice are involved.     

Elastic building blocks for confined sheets

We study the behavior of thin elastic sheets that are bent and strained under a weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains. A focused-stress patch is subject to a geometric, piecewise-inextensibility constraint, whereas a diffuse-stress region is characterized by a mechanical constraint-the dominance of a single component of the stress tensor. We discuss the implications of our findings for the analysis of elastic sheets under various types of forcing.     

Slow Motion and Metastability for a Nonlocal Evolution Equation

In this paper we consider a nonlocal evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean field approximation. In the presence of a small magnetic field, it admits two stationary and homogeneous solutions, representing the stable and metastable phases of the physical system. We prove the existence of an invariant, one dimensional manifold connecting the stable and metastable phases. This is the unstable manifold of a distinguished, spatially nonhomogeneous, stationary solution, called the critical droplet.^{(4, 10)} We show that the points on the manifold are droplets longer or shorter than the critical one, and that their motion is very slow in agreement with the theory of metastable patterns. We also obtain a new proof of the existence of the critical droplet, which is supplied with a local uniqueness result.     

Barriers in the p-spin interacting spin-glass model: the dynamical approach

We investigate the barriers separating metastable states in the spherical p-spin glass model using the instanton method. We show that the problem of finding the barrier heights can be reduced to the causal two-real-replica dynamics. We find the probability for the system to escape one of the highest energy metastable states and the energy barrier corresponding to this process.     

Phosphoinositide-binding interface proteins involved in shaping cell membranes

The mechanism by which cell and cell membrane shapes are created has long been a subject of great interest. Among the phosphoinositide-binding proteins, a group of proteins that can change the shape of membranes, in addition to the phosphoinositide-binding ability, has been found. These proteins, which contain membrane-deforming domains such as the BAR, EFC/F-BAR, and the IMD/I-BAR domains, led to inward-invaginated tubes or outward protrusions of the membrane, resulting in a variety of membrane shapes. Furthermore, these proteins not only bind to phosphoinositide, but also to the N-WASP/WAVE complex and the actin polymerization machinery, which generates a driving force to shape the membranes.     

Fluctuation-dissipation theorem for metastable systems

We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.     

Ear deformations give bats a physical mechanism for fast adaptation of ultrasonic beam patterns

A large number of mammals, including humans, have intricate outer ear shapes that diffract incoming sound in a direction- and frequency-specific manner. Through this physical process, the outer ear shapes encode sound-source information into the sensory signals from each ear. Our results show that horseshoe bats could dynamically control these diffraction processes through fast nonrigid ear deformations. The bats' ear shapes can alter between extreme configurations in about 100 ms and thereby change their acoustic properties in ways that would suit different acoustic sensing tasks.     

Light and thermally induced metastabilities in electrochemically etched nanocrystalline porous silicon

We observe that light soaking for short durations and thermal quenching in nanocrystalline porous silicon (PS) produce metastable states. These metastable states show higher dark and photo currents, large photoluminescence and a weaker electron spin resonance (ESR) signal. However, long exposures to light produce the opposite effect. The metastable states are stable against sub-band gap light exposures. These metastable states can be removed by annealing at 150°C for 1 h. ESR shows the presence of a-Si phase (g ～ 2.0058, 6.4 G) in PS sample, but it is not sufficient to explain all the experimental results. Rather, our experiments suggest that light soaking causes more than one type of defects in porous silicon. The structural changes involving the movement of hydrogen present at the surface of PS or at the PS/a-Si interface may be responsible for these effects.