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At least 73 records · Page 4

Phase-field model of freeze casting

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the ⟨0001⟩ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the ⟨0001⟩ directions. Here, we demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the ⟨0001⟩ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.

Materials science

Echo state network for coarsening dynamics of charge density waves

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDWs) in a semiclassical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Furthermore, our work opens avenues for efficient dynamical modeling of pattern formations in functional electron materials.

2-dimensional systems

Skyrmion-skyrmionium phase separation and laning transitions via spin-orbit torque currents

Many driven binary systems can exhibit laning transitions when the two species have different mobilities, such as colloidal particles with opposite charges in electric fields. Another example is pedestrian or active-matter systems, where particles moving in opposite directions form a phase-separated state that enhances the overall mobility. In this work, we use atomistic simulations to demonstrate that mixtures of skyrmions and skyrmioniums also exhibit pattern formation and laning transitions. Skyrmions move more slowly and at a finite skyrmion Hall angle compared to skyrmioniums, which move faster and without a skyrmion Hall effect. At low drives, the system forms a partially jammed phase where the skyrmioniums are dragged by the surrounding skyrmions, resulting in a finite angle of motion for the skyrmioniums. At higher drives, the system transitions into a laned state, but unlike colloidal systems, the lanes in the skyrmion-skyrmionium mixture are tilted relative to the driving direction due to the intrinsic skyrmion Hall angle. In the laned state, the skyrmionium angle of motion is reversed when it aligns with the tilted lane structure. At even higher drives, the skyrmioniums collapse into skyrmions. Below a critical skyrmion density, both textures can move independently with few collisions, but above this density, the laning state disappears entirely, and the system transitions to a skyrmion-only state. We map out the velocity and Hall responses of the different textures and identify three distinct phases: partially jammed, laned, and skyrmion-only moving crystal states. In conclusion, we compare our results to recent observations of tilted laning phases in pedestrian flows, where chiral symmetry breaking in the particle interactions leads to similar behavior.

36 MATERIALS SCIENCE

A stochastic model of the electromyogram

The quantitative regularities of interference pattern formation by motor unit action potentials is investigated. The parameters of a single motor unit and how they relate to the Fourier transform analysis of an EMG are considered. The Fourier transform of the simulated electromyogram is compared with the Fourier transform of the actual EMG recorded from various human muscles using surface electrodes.

Agarwal, G. C.

Primary instabilities and bicriticality in flow between counter-rotating cylinders

The primary instabilities and bicritical curves for flow between counter-rotating cylinders have been computed numerically from the Navier-Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40-0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter-rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m + 1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occurring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.

Langford, W. F.

A biosensor for cadmium based on bioconvective patterns

An 'in vitro' method for monitoring cadmium, one of the most lethal bivalent heavy metals, can detect biologically active levels. The effects of cadmium tend to concentrate in protozoa far above natural levels and therein begin transferring through freshwater food chains to animals and humans. In a small sample volume (approximately 5 ml) the method uses the toxic response to the protozoa, Tetrahymena pyriformis, to cadmium. The assay relies on macroscopic bioconvective patterns to measure the toxic response, giving a sensitivity better than 1 micro-g/1 and a toxicity threshold to 7 micro-g/1 for Cd(2+). Cadmium hinders pattern formation in a dose-dependent manner. Arrested organism growth arises from slowed division and mutation to non-dividing classes. Unlike previous efforts, this method can be performed in a shallow flow device and does not require electronic or chemical analyses to monitor toxicity.

Noever, David A.

An analysis of the moon's surface using reflected illumination from the earth during a waning crescent lunar phase

There have been many articles written concerning the lunar after-glow, the spectacular reflection from the moon's surface, and the possible observation of luminescence on the dark side of the moon. The researcher, using a 600 mm cassegrain telescope lense and Kodak 400 ASA T-Max film, photographed the crescent moon whose dark side was clearly visible by the reflected light from earth. The film was digitized to a Perkin-Elmer 1010M microdensitometer for enhancement and enlargement. The resulting pictures indicate a completely different land pattern formation than observed during a full moon. An attempt is made to analyze the observed structures and to compare them to the pictures observed during the normal full moon. There are boundaries on the digitized dark section of the moon that can be identified with structures seen during the normal full moon. But, these variations do change considerably under enhancement.

Hammond, Ernest C., Jr.

Interfacial wave theory of dendrite growth - Global mode solution and quantum condition

The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.

Xu, Jian-Jun

Shape selection criterion for cellular array during constrained growth of binary alloys - Need for low gravity experiment

Development of steady-state periodic cellular array is one of the critical problems in the study of nonlinear pattern formation during directional solidification of binary alloys. The criterion which establishes the values of cell tip radius and spacing under given growth condition is not known. Theoretical models, such as marginal stability and microscopic solvability, have been developed for purely diffusive regime. However, the experimental conditions where cellular structures are stable are precisely the ones where the convection effects are predominant. Thus, the critical data for meaningful evaluation of cellular array growth models can only be obtained by partial directional solidification and quenching experiments carried out in the low gravity environment of space.

Tewari, Surendra N.

Computations of drop collision and coalescence

Computations of drops collision and coalescence are presented. The computations are made possible by a recently developed finite difference/front tracking technique that allows direct solutions of the Navier-Stokes equations for a multi-fluid system with complex, unsteady internal boundaries. This method has been used to examine the boundaries between the various collision modes for drops of equal size and two examples, one of a 'reflective' collision and another of a 'grazing' collision is shown. From drops of unequal size, coalescence can result in considerable mixing between the fluid from the small and the large drop. This problem is discussed and one example showed. In many cases it is necessary to account also for heat transfer along with the fluid mechanics. We show two preliminary results where we are using extensions of the method to simulate such a problem. One example shows pattern formation among many drops moving due to thermal migration, the other shows unstable evolution of a solidification front.

Tryggvason, Gretar

Orbital Processing of Eutectic Rod-Like Arrays

The eutectic is one of only three solidification classes that exist. The others are isostructural and peritectic-class reactions, respectively. Simplistically, in a binaryeutectic phase diagram, a single liquid phase isothermally decomposes to two solid phases in a cooperative manner. The melting point minimum at the eutectic composition, isothermal solidification temperature, near-isocompositional solidification and refined solidification microstructure lend themselves naturally to such applications as brazing and soldering; industries that eutectic alloys dominate. Interest in direct process control of microstructures has led, more recently, to in-situ eutectic directional solidification with applications in electro-magnetics and electro-optics. In these cases, controlled structural refinement and the high aspect ratio and regularity of the distributed eutectic phases is highly significant to the fabrication and application of these in-situ natural composites. The natural pattern formation and scaling of the dispersed phase on a sub-micron scale has enormous potential application, since fabricating bulk materials on this scale mechanically has proven to be particularly difficult. It is thus of obvious importance to understand the solidification of eutectic materials since they are of great commercial significance. The dominant theory that describes eutectic solidification was derived for diffusion-controlled growth of alloys where both solid eutectic phases solidify metallically, i.e. without faceting at the solidification interface. Both high volume fraction (lamellar) and low volume fraction (rod-like) regular metallic arrays are treated by this theory. Many of the useful solders and brazements, however, and most of the regular in-situ composites are characterized by solidification reactions that are faceted/non-faceted in nature, rather than doubly non-faceted (metallic). Further, diffusion-controlled growth conditions are atypical terrestrially since gravitationally-driven convection is pervasive. As a consequence, it is important to determine whether these faceted/non-faceted composites behave in the same manner as their doubly non-faceted counterparts, particularly in the presence of convection. Prior analytical convective sensitivity testing of this theory predicted insensitivity. Prior experimental testing of this theory offered broad-based agreement between theory and experiment, though most results were for high volume fraction lamellar eutectics that solidified without faceting at the solidification interface. Directional solidification experiments of low volume fraction rod eutectics under damped (microgravity or magnetic field) conditions, however, have demonstrated significant sensitivity, challenging this fundamental theory. More recent theories have been proposed which introduce kinetic undercooling, faceting, fluid shear of the solute redistribution zone and the possibility that the interface composition is not the same as the bulk liquid composition. This program tests the established and proposed analytical theories and addresses the origins of discrepancies between the experimental and analytical results.

Larson, David J., Jr.

Materials Science Experiments on the International Space Station

The Performance Goal for NASA's Microgravity Materials Science Program reads "Use microgravity to establish and improve quantitative and predictive relationships between the structure, processing and properties of materials." The advent of the International Space Station will open up a new era in Materials Science Research including the ability to perform long term and frequent experiments in microgravity. As indicated the objective is to gain a greater understanding of issues of materials science in an environment in which the force of gravity can be effectively switched off. Thus gravity related issues of convection, buoyancy and hydrostatic forces can be reduced and the science behind the structure/processing/properties relationship can more easily be understood. The specific areas of research covered within the program are (1) the study of Nucleation and Metastable States, (2) Prediction and Control of Microstructure (including pattern formation and morphological stability), (3) Phase Separation and Interfacial Stability, (4) Transport Phenomena (including process modeling and thermophysical properties measurement), and (5) Crystal Growth, and Defect Generation and Control. All classes of materials, including metals and alloys, glasses and ceramics, polymers, electronic materials (including organic and inorganic single crystals), aerogels and nanostructures, are included in these areas. The principal experimental equipment available to the materials scientist on the International Space Station (ISS) will be the Materials Science Research Facility (MSRF). Each of these systems will be accommodated in a single ISS rack, which can operate autonomously, will accommodate telescience operations, and will provide real time data to the ground. Eventual plans call for three MSRF racks, the first of which will be shared with the European Space Agency (ESA). Under international agreements, ESA and other partners will provide some of the equipment, while NASA covers launch and integration costs. The MSRF facilities will include modular components, which can be exchanged to provide inserts specifically matched to the engineering requirements of the particular Principal Investigator. To defray costs and avoid duplication of engineering effort NASA is also pursuing the possibility of using facilities provided by international partners. By this means it is anticipated that all of the types of research outlined in the previous paragraph can be done on the ISS.

Gillies, Donald C.

The Isothermal Dendritic Growth Experiment (IDGE): USMP-4 One-Year-Report

Dendrites describe the tree-like crystal morphology commonly assumed in many material systems--particularly in metals and alloys that freeze from supercooled or supersaturated melts. There remains a high level of engineering interest in dendritic solidification because of the role of dendrites in the determination of cast alloy microstructures. Microstructure plays a key role in determining the physical properties of cast or welded products. In addition, dendritic solidification provides an example of non-equilibrium physics and is one of the simplest non-trivial examples of dynamic pattern formation, where an amorphous melt, under simple starting conditions, evolves into a complex ramified microstructure. Although it is well-known that dendritic growth is controlled by the transport of latent heat from the moving solid-melt interface as the dendrite advances into a supercooled melt, an accurate, and predictive model has not been developed. Current theories consider: 1) the transfer of heat or solute from the solid-liquid interface into the melt, and 2) the interfacial crystal growth and growth selection physics for the interface. However, the effects of gravity-induced convection on the transfer of heat from the interface prevent either element from being adequately tested solely under terrestrial conditions. The Isothermal Dendritic Growth Experiment (IDGE) constituted a series of three NASA-supported microgravity experiments, all of which flew aboard the space shuttle, Columbia. This experimental space flight series was designed and operated to grow and record dendrite solidification in the absence of gravity-induced convective heat transfer, and thereby produce a wealth of benchmark-quality data for testing solidification scaling laws. The data collection from the on-orbit phase of the IDGE flight series is now complete. We are currently completing analyses and moving towards final data archiving.

Glicksman, M. E.

Ground-Based Experiments on Vibrational Thermal Convection

Ground-based experiments on g-jitter effects in fluid flow provide insight that complements both theoretical studies and space-based experiments on this problem. We report preliminary results for experiments on Rayleigh-Benard convection subjected to time-dependent accelerations on a shaker table. For sinusoidal modulation, two qualitatively different pattern forming mechanisms come into play: geometry induced wavenumber selection (as in the standard "no-shake" Rayleigh-Benard problem) and dispersion induced wavenumber selection due to parametric instability (as in the Faraday surface-wave problem). We discuss preliminary results on the competition and co-existence of patterns due to these different instability mechanisms. We also discuss the implications of this work on the general question of pattern formation in the presence of noise.

Schatz, Michael F.

Cellular Spacing Selection During the Directional Solidification of Binary Alloys. A Numerical Approach

The evolution of cellular solid/liquid interfaces from an initially unstable planar front was studied by means of a two-dimensional computer simulation. The developed numerical model makes use of an interface tracking procedure and has the capability to describe the dynamics of the interface morphology based on local changes of the thermodynamic conditions. The fundamental physics of this formulation was validated against experimental microgravity results and the predictions of the analytical linear stability theory. The performed simulations revealed that in certain conditions, based on a competitive growth mechanism, an interface could become unstable to random perturbations of infinitesimal amplitude even at wavelengths smaller than the neutral wavelength, lambda(sub c), predicted by the linear stability theory. Furthermore, two main stages of spacing selection have been identified. In the first stage, at low perturbations amplitude, the selection mechanism is driven by the maximum growth rate of instabilities while in the second stage the selection is influenced by nonlinear phenomena caused by the interactions between the neighboring cells. Comparison of these predictions with other existing theories of pattern formation and experimental results will be discussed.

Catalina, Adrian V.

The Transient Dendritic Solidification Experiment (TDSE)

Dendritic solidification is a common mode of solidification. It is also an important model problem in nonequilibrium physics and pattern formation physics. Current theories couple the transfer of latent heat with selection mechanisms at the interface. Measurements of succinonitrile (SCN) dendrites in microgravity show reasonable agreement between heat transfer predictions and experiment. However, data and analysis for assessing interfacial physics theories are less definitive. We are studying, and will present data on, transient effects in dendritic growth of SCN. We employ the Clapeyron pressure/melting temperature effect to make a rapid change in a sample's hydrostatic pressure, and thereby rapidly change the specimen's melting temperature, forcing the dendrite to select a new steady-state. These initial measurements show some surprising and non-intuitive effects.

Koss, M. B.

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.