Saddle Configurations Research Articles

High-stiffness reconfigurable surfaces based on bistable element assembly and bi-compatible truss attachment

Reconfigurable surfaces contribute to multi-task robotic platforms, such as reconfigurable phased array antennas with variable aperture, by morphing between multiple specified shapes. Controlling each tile to approximate the variating shape of target surfaces requires a large number of accurate actuators. Previous research has demonstrated employing bistable-element-assembly to form reconfigurable surfaces for significant actuation simplification but suffering from low out-of-plane stiffness resulting in the lack of load-bearing capacity for carrying functional units with good mechanical accuracy. This paper proposes a design framework for tile-assembling bistable (TAB) surfaces with bi-compatible truss attachment for two prescribable stable configurations. The bistability comes from joining surface tiles with bistable elements, which contributes to easy actuation with fewer inaccurate actuators. Bi-compatible truss structures, which are only kinematically compatible at the two prescribed states, are introduced to enhance the out-of-plane stiffness of the TAB surface and improve its load-bearing capacity. Additionally and consequently, the kinematic determinacy of the reconfigurable surfaces is increased by the truss introduction, where bistable elements control the metric while truss structures dictate the principal curvature of the surface. This diminishes the redundant degrees of freedom with enhanced shape-approximation and reconfiguration-coordination. Four prototypes are designed and manufactured, which are a three-tile by three-tile (3 × 3) TAB surface that is stable at flat and spherical configurations, a 5 × 5 TAB surface with flat and spherical stable configurations, a 3 × 3 TAB surface that is stable at the flat and saddle configurations, and a 3 × 3 TAB surface that is stable at the sphere and saddle shapes. The out-of-plane stiffness, easiness of actuation, and shape accuracy of all prototypes are evaluated and show promises for real engineering applications.

Atomistic mechanisms of phase nucleation and propagation in a model two-dimensional system

We present a computational study on the solid–solid phase transition of a model two-dimensional system between hexagonal and square phases under pressure. The atomistic mechanism of phase nucleation and propagation are determined using solid-state Dimer and nudged elastic band (NEB) methods. The Dimer is applied to identify the saddle configurations and NEB is applied to generate the transition minimum energy path (MEP) using the outputs of Dimer. Both the atomic and cell degrees of freedom are used in saddle search, allowing us to capture the critical nuclei with relatively small supercells. It is found that the phase nucleation in the model material is triggered by the localized shear deformation that comes from the relative shift between two adjacent atomic layers. In addition to the conventional layer-by-layer phase propagation, an interesting defect-assisted low barrier propagation path is identified in the hexagonal to square phase transition. The study demonstrates the significance of using the Dimer method in exploring unknown transition paths without a priori assumption. The results of this study also shed light on phase transition mechanisms of other solid-state and colloidal systems.

Numerical investigation of dislocation climb under stress and irradiation

We investigate the influence of elastic properties of point defects on dislocation climb under stress and irradiation. For this purpose, elastic dipole tensors and diaelastic polarizabilities are evaluated in aluminum for vacancies and self-interstitial atoms in their stable and saddle configurations, using density functional theory calculations. These parameters are introduced in an object kinetic Monte-Carlo code and a continuous diffusion model to estimate the stress dependence of dislocation climb, using a dipole of straight dislocations. We show that both parameters have an influence on absorption of point defects under stress, in agreement with previous analytical models. However, the effect of dipole tensor is found only 5 times larger than polarizability, whereas models predict a factor up to 30. In addition, including polarizability reverses the stress angular dependence when a uniaxial stress is applied orthogonal to the dislocation line, so in general polarizability cannot be ignored for simulations under applied stress. Further comparison with analytical models shows that they give a good description of angular dependence, provided saddle point configuration of point defects is not too anisotropic. For vacancies, which are strongly anisotropic in their saddle configuration, models fail to reproduce quantitatively lattice effects on stress angular dependence observed in simulations. Calculations show that dislocation climb velocity under irradiation is expected to be the highest if the stress is approximately orthogonal to the dislocation line, especially along the Burgers vector, and the lowest if the stress is applied close to the 〈100〉 direction with the largest projection on the dislocation line.

Dimerization dynamics of carboxylic acids in helium nanodroplets.

The dimerization of molecules in helium nanodroplets is known to preferentially yield structures of higher energy than the global energy minimum structure for a number of quite different monomers. Here, we explore dimerization in this environment using an atomistic model within statistically converged molecular dynamics (MD) trajectories, treating the solvent implicitly through the use of a thermostat, or more explicitly by embedding one monomer in a He100 cluster. The focus is on the two simplest carboxylic acids, formic and acetic, both of which have been studied experimentally. While the global minimum structure, which comprises two CO⋯HO hydrogen bonds, is predicted to be the most abundant dimer in the absence of the helium solvent, this is no longer the case once helium atoms are included. The simulations confirm the importance of kinetic trapping effects and also shed light on the occurrence of specific dynamical effects, leading to the occasional formation of high-energy structures away from minima, such as saddle configurations. Theoretically predicted infrared spectra, based on the MD statistics, are in good agreement with the experimental spectra.

Metastability of Blume–Capel Model with Zero Chemical Potential and Zero External Field

In this study, we investigate the metastable behavior of Metropolis-type Glauber dynamics associated with the Blume-Capel model with zero chemical potential and zero external field at very low temperatures. The corresponding analyses for the same model with zero chemical potential and positive small external field were performed in [Cirillo and Nardi, Journal of Statistical Physics, 150: 1080-1114, 2013] and [Landim and Lemire, Journal of Statistical Physics, 164: 346-376, 2016]. We obtain both large deviation-type and potential-theoretic results on the metastable behavior in our setting. To this end, we perform highly thorough investigation on the energy landscape, where it is revealed that no critical configurations exist and alternatively a massive flat plateau of saddle configurations resides therein.

Two-dimensional overdamped simulations of droplet solitons activated by spin transfer torque

We present overdamped micromagnetic simulations of the time evolution of magnetic droplet solitons which are formed in a thin film with perpendicular magnetic anisotropy by injecting a spin polarized current through a circular nanocontact. The overdamped dynamics help explore the effective energy landscape of these structures and permit identification of stationary states that are either energy extrema or saddle configurations. Our micromagnetic simulations start with configurations that are numerical solutions of a one-dimensional model where the magnetization depends only on the radial distance to the center of the nanocontact. We verify that these solutions correspond either to energy minima or saddle states, and use them to estimate thermal activation barriers for various current strengths. From the two-dimensional micromagnetic simulations, we identify a new persistent state which does not appear in the one-dimensional model.

Physical resurgent extrapolation

Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this idea mathematically, and leads to significantly more powerful extrapolation methods to extract physical information from a finite number of terms of an expansion, including precise decoding of non-perturbative effects. We quantify the gain of precision for various extrapolation procedures, showing that significant improvements can be achieved using exactly the same input data, and we illustrate the general method with examples from quantum mechanics and quantum field theory.

Generic power supply feedback controller for control of plasma parameters in SST-1

Steady State Superconducting Tokamak (SST-1) uses Radial Control Coil (RCC) for radial control of the plasma in initial experiments. RCC is a resistive single turn coil. There are two radial coils placed symmetrically up and down. These coils are connected either in saddle or parallel configurations. The requirement of rate of rise of current in RCC is 1 MA/s with peak current as ±10 kA. The power supply consists of IGBT based 72 H bridge inverter modules connected in parallel, L-C filter, 12 pulse SCR rectifier circuit, water cooling system and transformer. A versa module euro card (VME) bus based Generic Controller (GC) has been developed to control current in RCC in feedback loop. GC controls gate pulse firing of 72 IGBT based H bridge inverter module using hysteresis band control. GC provides 2.5 kHz to 10 kHz switching with fiber optic gate pulse interface to RCC power supply. This paper describes existing controller along with associated issues, development of VME bus based GC, its hardware and software with flow chart, RTOS VxWorks programming, integration of GC with H bridge inverter, MATLAB simulation, testing results of random and step perturbation with power supply operations.

Saddle Height and Cadence Effects on the Physiological, Perceptual, and Affective Responses of Recreational Cyclists.

Saddle height influences cycling performance and would be expected to influence cyclists physically, perceptually, and emotionally. We investigated how different saddle positions and cadences might affect cyclists' torque, heart rate, rate of perceived exertion (RPE), and affective responses (Feeling scale). Nine male recreational cyclists underwent cycling sessions on different days under different conditions with a constant load. On Day 1, the saddle was at the reference position (109% of the distance from the pubic symphysis to the ground), and on Days 2 and 3, the saddle was in the "upward position" (reference + 2.5%) and "downward position" (reference - 2.5%) in random order. Each session lasted 30 minutes and was divided into three cadence-varied 10-minute stages without interruption: (a) freely chosen cadence (FCC), (b) FCC - 20%, and (c) FCC + 20%. We assessed all dependent measures at the end of each 10 minute stage. While there was no significant interaction (Saddle × Cadence) for any of the analyzed variables, torque values were higher at lower cadences in all saddle configurations, and the FCC + 20% cadence was associated with faster heart rate, higher RPE, and lower affect compared with FCC and FCC - 20% in all saddle positions. At all cadences, the saddle at "downward position" generated a higher RPE compared with "reference position" and "upward position." The affective response was lower in the "downward position" compared with the "reference position." Thus, while cyclists perceived the downward (versus reference) saddle position as greater exercise effort, they also associated it with unpleasant affect.

Hydrogen influence on diffusion in nickel from first-principles calculations

We propose a method to evaluate the diffusion coefficient of vacancy-hydrogen clusters (${\mathrm{VH}}_{n})$ in metals. The key is a good separation of time scales between H diffusion and the metal-vacancy exchange. The Ni-H system is investigated in details, using ab initio calculations, but the arguments can be transposed to other systems. It is shown that cluster diffusion can be treated as an uncorrelated random walk and that H is always in equilibrium before the vacancy-metal exchange. Then, the diffusion coefficient is a sum over jump paths of the equilibrium probability of being in a specific ${\mathrm{VH}}_{n}$ configuration times the corresponding activation terms. The influence of H on the energy barrier is well reproduced by effective pair interactions between the jumping Ni and the H atoms inside the vacancy. This model is motivated by an analysis of the electronic charge redistribution in key saddle configurations. The interaction is repulsive and decreases with distance. The model is used to find easy jump path, reduce the number of saddle searches, and provide an estimate of the error expected from this reduction. The application to the Ni-H system shows that vacancies are drastically slowed down by H. The effects of temperature and bulk H concentration are explored and the origin of the non-Arrhenius behavior is explained. At equilibrium, ${\mathrm{VH}}_{n}$ clusters always induce a speedup of metal diffusion. The implications concerning H induced damage, in particular in regards to Ni-Cr oxidation, are discussed.

On smooth foliations with Morse singularities

Let M be a smooth manifold and let F be a codimension one, C∞ foliation on M, with isolated singularities of Morse type. The study and classification of pairs (M,F) is a challenging (and difficult) problem. In this setting, a classical result due to Reeb (1946) [11] states that a manifold admitting a foliation with exactly two center-type singularities is a sphere. In particular this is true if the foliation is given by a function. Along these lines a result due to Eells and Kuiper (1962) [4] classifies manifolds having a real-valued function admitting exactly three non-degenerate singular points. In the present paper, we prove a generalization of the above mentioned results. To do this, we first describe the possible arrangements of pairs of singularities and the corresponding codimension one invariant sets, and then we give an elimination procedure for suitable center–saddle and some saddle–saddle configurations (of consecutive indices).In the second part, we investigate if other classical results, such as Haefliger and Novikov (Compact Leaf) theorems, proved for regular foliations, still hold true in presence of singularities. At this purpose, in the singular set, Sing(F) of the foliation F, we consider weakly stable components, that we define as those components admitting a neighborhood where all leaves are compact. If Sing(F) admits only weakly stable components, given by smoothly embedded curves diffeomorphic to S1, we are able to extend Haefligerʼs theorem. Finally, the existence of a closed curve, transverse to the foliation, leads us to state a Novikov-type result.

Small interstitials clusters migration in bcc metals: A Molybdenum model

The migration mechanisms of small self-interstitial clusters in two models for bcc Molybdenum are studied by computer simulation. The research is pertinent to the stages after collision cascade collapse of radiation damage, when defects diffuse to sinks and agglomerate into bigger units. Among the interaction models considered, one is a rather standard many-body central forces potential; the other one includes angle contributions to the energy, which in principle is a more consistent representation of a bcc transition metal. Also, two techniques are employed: Molecular Dynamics and Monomer. The former provides global parameters of the diffusion process; the latter is a static technique to search the potential energy surface for saddle configurations, thus providing detailed information on transition events. Reasonable agreement is found among the techniques, though the connection between the static parameters with the dynamic ones may not be straightforward. The two interaction models result in both quantitative and qualitative differences; notably in some cases when the former are small the underlying microscopic mechanisms can be nevertheless different.

Interaction of intrinsic point defects with dislocation stress fields in hcp zirconium crystal

The crystallographic, energetic, and kinetic characteristics of intrinsic point defects (vacancy-self-interstitial atom) in stable, metastable, and saddle configurations in hcp zirconium crystal have been calculated by the molecular-statics method. The spatial dependences of the interaction energies of intrinsic point defects and stress fields of rectilinear dislocations with Burgers vectors of 1/3[11\( \bar 2 \)0], 1/3 [11\( \bar 2 \)3], and [0001] have been found within the anisotropic linear theory of elasticity. The most likely trajectories of intrinsic point defects in dislocation stress fields (trajectories with minimum energy barriers for motion) have been constructed. Such trajectories result in dislocation only for the interaction of self-interstitial atoms with an edge dislocation that has a Burgers vector of 1/3 [11\( \bar 2 \)3].

Stress-dependent Peierls potential: Influence on kink-pair activation

Atomistic calculations based on the nudged elastic band method for a Lomer dislocation in aluminum evidence a dependence of the Peierls potential on the applied shear stress in such a way that the Peierls stress predicted from the zero-stress potential is half its true value for the case considered here. Stress-dependent Peierls potentials that are extracted are then introduced as substrate potentials in a string model with a line tension (LT) adjusted to match the dislocation kink width obtained from atomistic simulations. The LT model is found to predict accurately dislocation saddle configurations and corresponding kink-pair activation enthalpies for a wide range of stresses. In particular, it is shown that the stress dependence of the Peierls potential is required to model with accuracy the nonlinearity of the enthalpy-stress curve.

Self-assembly and ordering mechanisms of Ge islands on prepatterned Si(001)

Ge deposition on Si(001) substrates patterned by focused ion beams is a promising route toward fabricating highly ordered quantum dots. Depending on the growth temperature $T$, remarkable orderings of the assembled islands are observed. At low $T$'s, when diffusion is limited, a metastable phase with dots nucleating in the holes prevails. At high $T$'s, when diffusion is not limited by kinetics, an equilibrium ordered phase is observed with dots nucleating on the terraces in between the pits. At intermediate $T$'s, random growth arises. Monte Carlo simulations shed light onto this phenomenon. It is shown that the average stress energy of the equilibrium ordered configuration is significantly lower than the energy of configurations with islands positioned in the pits. Random nucleation gives rise to saddle configurations between the two ordered phases.

Micromagnetic simulations of ferromagnetic rings

Thin nanomagnetic rings have generated interest for fundamental studies of magnetization reversal and also for their potential in various applications, particularly as magnetic memories. They are a rare example of a geometry in which an analytical solution for the rate of thermally induced magnetic reversal has been determined, in an approximation whose errors can be estimated and bounded. In this work, numerical simulations of soft ferromagnetic rings are used to explore aspects of the analytical solution. The evolution of the energy near the transition states confirms that, consistent with analytical predictions, thermally induced magnetization reversal can have one of two intermediate states: either constant or solitonlike saddle configurations, depending on ring size and externally applied magnetic field. The results confirm analytical predictions of a transition in thermally activated reversal behavior as magnetic field is varied at constant ring size. Simulations also show that the analytic one-dimensional model continues to hold even for wide rings.

Determining landscape-based criteria for freezing of liquids

The correlation between statistical properties of the energy landscape and the number of accessible configurational states, as measured by the exponential of the excess entropy (e(Se)), are studied in the case of a simple Lennard-Jones-type liquid in the neighborhood of the thermodynamic freezing transition. The excess entropy Se is defined as the difference between the entropy of the liquid and that of the ideal gas under identical temperature and pressure conditions and is estimated using the pair correlation contribution, S2. Landscape properties associated with three categories of configurations are considered: instantaneous configurations, inherent saddles, and inherent minima. Landscape properties studied include the energy and the key parameters of the Hessian eigenvalue distribution as well as the mean distances between instantaneous configurations and the corresponding inherent saddles and minima. The signatures of the thermodynamic freezing transition are clearest in the case of inherent structure properties which show, as a function of e(S2), a pronounced change in slope in the vicinity of the solid-liquid coexistence. The mean distance between instantaneous and saddle configurations also shows a similar change in slope when the system crosses from the stable to the supercooled regime. In the case of inherent saddles, the minimum eigenvalue acts as a similar indicator of the thermodynamic freezing transition but the average and maximum eigenvalues do not carry similar signatures. In the case of instantaneous configurations, a weak indicator of the thermodynamic freezing transition is seen in the behavior of the fraction of negative curvature directions as a function of the exponential of the excess entropy.

Search of point defect transition states in hcp twin boundaries: The monomer method

We develop the monomer, a molecular statics technique for the search of transition states under conditions of relatively complex atomistic environments. As its counterpart from the literature, the dimer, our method is based on forces evaluation alone and is able to find the saddle configuration without previous knowledge of the equilibrium state across the saddle; at variance with it, the needed local curvature is determined with just one force evaluation per iteration step. The method is here applied to the location of saddle configurations relevant to the migration of vacancies and self-interstitials in the $(11\overline{2}1)$ and $(11\overline{2}2)$ twin boundaries of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Zr}$ modeled with an embedded atom type interatomic potential. Besides the fundamental interest of studying migration in these environments of reduced symmetry and dimensionality, we aim at a better understanding of grain boundaries as agents contributing to the mechanical deformation under irradiation conditions. Whereas vacancies have already been studied in the same boundaries employing a different methodology, self-interstitial results are new. For comparison purposes and completeness however, some results relating to vacancies are also included. Our main findings relate to the prediction of very low interstitial migration energies that radically change the anisotropy of bulk migration. This behavior may be associated, though not necessarily, with spatially extended configurations. The results suggest that the picture of grain boundaries as essentially perfect sinks, common to models of irradiation creep and growth, may need revision.

Diffusivity, excess entropy, and the potential-energy landscape of monatomic liquids

The connection between thermodynamic, transport, and potential-energy landscape features is studied for liquids with Lennard-Jones-type pair interactions using both microcanonical molecular-dynamics and isothermal-isobaric ensemble Monte Carlo simulations. Instantaneous normal-mode and saddle-point analyses of two variants of the monatomic Lennard-Jones liquid have been performed. The diffusivity is shown to depend linearly on several key properties of instantaneous and saddle configurations-the energy, the fraction of negative curvature directions, and the mean, maximum, and minimum eigenvalues of the Hessian. Since the Dzugutov scaling relationship also holds for such systems [Nature (London) 381, 137 (1996)], the exponential of the excess entropy, within the two-particle approximation, displays the same linear dependence on energy landscape properties as the diffusivity.

Comparison of inherent, instantaneous, and saddle configurations of the bulk Lennard-Jones system

The configurational energies, order parameters and normal mode spectra associated with inherent structure, inherent saddle, and instantaneous configurations of the bulk Lennard-Jones system are compared. Instantaneous structures are generated by sampling configurations from an isothermalisobaric ensemble Monte Carlo simulation. Local minimization of the potential, starting from a given instantaneous configuration is used to determine the corresponding inherent structure. The inherent saddles are obtained by local minimization on a pseudo-potential surface defined in terms of the square magnitude of the potential gradient. In the solid phase, no stationary points of order greater than zero are sampled and minimizations of both the potential, as well as of the pseudo-potential, always lead to the same global minimum energy crystalline configuration. The energies of instantaneous configurations of the solid show a clear negative correlation with the second-order bond orientational parameters. The instantaneous normal mode spectrum of the solid close to melting has a fairly prominent imaginary branch and is sufficiently smoothed out by local disorder that it qualitatively resembles the liquid phase INM spectrum. In the liquid phase, the inherent, saddle, and instantaneous structures form distinct sets of configurations. The thermal averages of the saddle energies and force constants lie between that of the instantaneous and inherent structures. The temperature dependence of the mean saddle energy and force constant is essentially parallel to that of the corresponding instantaneous quantities. The fraction of imaginary modes for the saddle configurations is approximately half that of the instantaneous configurations. The most striking similarity between the instantaneous and saddle configurations is the linear relationship between the index density and the configurational energy. The most notable difference between the two sets of configurations is the reduction to zero of the fraction of imaginary modes of the saddle configurations on freezing, making the saddle normal mode spectra qualitatively different in the liquid and solid phases.