Basic Understanding of Condensed Phases of Matter via Packing Models

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298

Medial Skeletal Diagram: A Generalized Medial Axis Approach for Compact 3D Shape Representation

We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around compactness and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous elements in the medial axis representation to effectively shift the complexity away from discrete elements. To that end, we introduce generalized enveloping primitives, an enhancement of the standard primitives in medial axis, which ensures efficient coverage of intricate local features of the input shape and substantially reduces the number of discrete elements required. Moreover, we present a computational framework that constructs a medial skeletal diagram from an arbitrary closed manifold mesh. Our optimization pipeline ensures that the resulting medial skeletal diagram comprehensively covers the input shape with the fewest primitives. Additionally, each optimized primitive undergoes a post-refinement process to guarantee an accurate match with the source mesh in both geometry and tessellation. We validate our approach on a comprehensive benchmark of 100 shapes, demonstrating its compactness of the discrete elements and superior reconstruction accuracy across a variety of cases. Furthermore, we exemplify the versatility of our representation in downstream applications such as shape optimization, shape generation, mesh decomposition, mesh alignment, mesh compression, and user-interactive design.Comment: 22 pages, 28 figure

Hi-Fidelity Simulation of the Self-Assembly and Dynamics of Colloids and Polymeric Solutions with Long Range Interactions

Modeling the equilibrium properties and dynamic response of the colloidal and polymeric solutions provides valuable insight into numerous biological and industrial processes and facilitates development of novel technologies. To this end, the centerpiece of this research is to incorporate the long range electrostatic or hydrodynamic interactions via computationally efficient algorithms and to investigate the effect of these interactions on the self-assembly of colloidal particles and dynamic properties of polymeric solutions. Specifically, self-assembly of a new class of materials, namely bipolar Janus nano-particles, is investigated via molecular dynamic simulation in order to establish the relationship between individual particle characteristics, such as surface charge density, particle size, etc., and the final structure formation. Furthermore, the importance of incorporating the long range electrostatic interaction in achieving the corresponding final morphology is discussed. The dynamic properties of polymeric solutions are investigated via two parallel pathways. In the first approach, force-extension behavior of the flexible polyelectrolytes is probed via fine-grained Brownian dynamics simulation of the bead-rod model. The presented model accurately incorporates the excluded volume interaction in order to capture the effect of salt concentration on the force-extension response of polyelectrolyte chain as observed in the single chain experiments. It is shown that accurate incorporation of the excluded volume effect on a long chain of more than 500 Kuhn segments is necessary to reach the universal scaling both for equilibrium properties and force-extension response. Next, a new force law is extracted using a novel discrete Pade approximant from the constant-force ensemble result of the bead-rod model. The new force law is implemented in the coarse-grained meso-scale bead-spring model with hydrodynamic interactions in order to investigate the dynamics of flexible macromolecules in the athermal solvent. In the second approach the computational cost of the long range hydrodynamic interaction in dilute solution of polymeric chains with constrains is reduced via development of a new computational technique based on the conjugate gradient and Krylov subspace methods. Moreover, an algorithm for estimating the contribution of various forces to the transient polymeric stress tensor is introduced and employed in order to investigate transient dynamics of the solution of the flexible polymeric chains

Adaptive Obstacle Avoidance for a Class of Collaborative Robots

In a human–robot collaboration scenario, operator safety is the main problem and must be guaranteed under all conditions. Collision avoidance control techniques are essential to improve operator safety and robot flexibility by preventing impacts that can occur between the robot and humans or with objects inadvertently left within the operational workspace. On this basis, collision avoidance algorithms for moving obstacles are presented in this paper: inspired by algorithms already developed by the authors for planar manipulators, algorithms are adapted for the 6-DOF collaborative manipulators by Universal Robots, and some new contributions are introduced. First, in this work, the safety region wrapping each link of the manipulator assumes a cylindrical shape whose radius varies according to the speed of the colliding obstacle, so that dynamical obstacles are avoided with increased safety regions in order to reduce the risk, whereas fixed obstacles allow us to use smaller safety regions, facilitating the motion of the robot. In addition, three different modalities for the collision avoidance control law are proposed, which differ in the type of motion admitted for the perturbation of the end-effector: the general mode allows for a 6-DOF perturbation, but restrictions can be imposed on the orientation part of the avoidance motion using 4-DOF or 3-DOF modes. In order to demonstrate the effectiveness of the control strategy, simulations with dynamic and fixed obstacles are presented and discussed. Simulations are also used to estimate the required computational effort in order to verify the transferability to a real system

Phenomenological modeling of image irradiance for non-Lambertian surfaces under natural illumination.

Various vision tasks are usually confronted by appearance variations due to changes of illumination. For instance, in a recognition system, it has been shown that the variability in human face appearance is owed to changes to lighting conditions rather than person\u27s identity. Theoretically, due to the arbitrariness of the lighting function, the space of all possible images of a fixed-pose object under all possible illumination conditions is infinite dimensional. Nonetheless, it has been proven that the set of images of a convex Lambertian surface under distant illumination lies near a low dimensional linear subspace. This result was also extended to include non-Lambertian objects with non-convex geometry. As such, vision applications, concerned with the recovery of illumination, reflectance or surface geometry from images, would benefit from a low-dimensional generative model which captures appearance variations w.r.t. illumination conditions and surface reflectance properties. This enables the formulation of such inverse problems as parameter estimation. Typically, subspace construction boils to performing a dimensionality reduction scheme, e.g. Principal Component Analysis (PCA), on a large set of (real/synthesized) images of object(s) of interest with fixed pose but different illumination conditions. However, this approach has two major problems. First, the acquired/rendered image ensemble should be statistically significant vis-a-vis capturing the full behavior of the sources of variations that is of interest, in particular illumination and reflectance. Second, the curse of dimensionality hinders numerical methods such as Singular Value Decomposition (SVD) which becomes intractable especially with large number of large-sized realizations in the image ensemble. One way to bypass the need of large image ensemble is to construct appearance subspaces using phenomenological models which capture appearance variations through mathematical abstraction of the reflection process. In particular, the harmonic expansion of the image irradiance equation can be used to derive an analytic subspace to represent images under fixed pose but different illumination conditions where the image irradiance equation has been formulated in a convolution framework. Due to their low-frequency nature, irradiance signals can be represented using low-order basis functions, where Spherical Harmonics (SH) has been extensively adopted. Typically, an ideal solution to the image irradiance (appearance) modeling problem should be able to incorporate complex illumination, cast shadows as well as realistic surface reflectance properties, while moving away from the simplifying assumptions of Lambertian reflectance and single-source distant illumination. By handling arbitrary complex illumination and non-Lambertian reflectance, the appearance model proposed in this dissertation moves the state of the art closer to the ideal solution. This work primarily addresses the geometrical compliance of the hemispherical basis for representing surface reflectance while presenting a compact, yet accurate representation for arbitrary materials. To maintain the plausibility of the resulting appearance, the proposed basis is constructed in a manner that satisfies the Helmholtz reciprocity property while avoiding high computational complexity. It is believed that having the illumination and surface reflectance represented in the spherical and hemispherical domains respectively, while complying with the physical properties of the surface reflectance would provide better approximation accuracy of image irradiance when compared to the representation in the spherical domain. Discounting subsurface scattering and surface emittance, this work proposes a surface reflectance basis, based on hemispherical harmonics (HSH), defined on the Cartesian product of the incoming and outgoing local hemispheres (i.e. w.r.t. surface points). This basis obeys physical properties of surface reflectance involving reciprocity and energy conservation. The basis functions are validated using analytical reflectance models as well as scattered reflectance measurements which might violate the Helmholtz reciprocity property (this can be filtered out through the process of projecting them on the subspace spanned by the proposed basis, where the reciprocity property is preserved in the least-squares sense). The image formation process of isotropic surfaces under arbitrary distant illumination is also formulated in the frequency space where the orthogonality relation between illumination and reflectance bases is encoded in what is termed as irradiance harmonics. Such harmonics decouple the effect of illumination and reflectance from the underlying pose and geometry. Further, a bilinear approach to analytically construct irradiance subspace is proposed in order to tackle the inherent problem of small-sample-size and curse of dimensionality. The process of finding the analytic subspace is posed as establishing a relation between its principal components and that of the irradiance harmonics basis functions. It is also shown how to incorporate prior information about natural illumination and real-world surface reflectance characteristics in order to capture the full behavior of complex illumination and non-Lambertian reflectance. The use of the presented theoretical framework to develop practical algorithms for shape recovery is further presented where the hitherto assumed Lambertian assumption is relaxed. With a single image of unknown general illumination, the underlying geometrical structure can be recovered while accounting explicitly for object reflectance characteristics (e.g. human skin types for facial images and teeth reflectance for human jaw reconstruction) as well as complex illumination conditions. Experiments on synthetic and real images illustrate the robustness of the proposed appearance model vis-a-vis illumination variation. Keywords: computer vision, computer graphics, shading, illumination modeling, reflectance representation, image irradiance, frequency space representations, {hemi)spherical harmonics, analytic bilinear PCA, model-based bilinear PCA, 3D shape reconstruction, statistical shape from shading

Anisotropic Particles: Preparation and Study

Anisotropic particles have received significant attention in self-assembly for the large scale fabrication of hierarchical structures. Janus particles, a specific class of anisotropic particles, have two hemispheres with different materials. Due to the anisotropic nature of the particle shape and interactions, Janus particles have demonstrated interesting properties in interfacial assembly, switchable devices, cargo transport, and optical sensing. The objective of this research is to fabricate novel anisotropic Janus particles and explore their potential unique properties.;One of the driving forces arises from the previous work of bimetallic nanorods and their autonomous motion. The bimetallic nanorod systems undergo chemically powered non- Brownian motion due to the asymmetric distribution of catalytic source for a chemical fuel solution. However, the approach used to prepare the bimetallic nanorods is rather complex. The original design of bimetallic Janus particles is based on a general physical vapor deposition technique -- electron beam evaporation. The resulting bimetallic Janus particles are colloidal silica spheres coated with two differing metals on each hemisphere. This approach allows fabricating bimetallic Janus particles with various combinations of metals that are available for electron beam evaporation.;Chemical transformation of bimetallic Janus particles into other species provides an opportunity to expand the scope of anisotropic particles. The metals on the Janus particles are possible to convert to their corresponding metal oxides and metal sulfides through solid-gas heterogeneous reactions, and therefore, the chemical transformation of the parent bimetallic Janus particles produces a wide array of previously unavailable Janus particle types, including metal/metal oxide, metal/metal sulfide, metal oxide/metal oxide, metal sulfide/metal sulfide, and metal oxide/metal sulfide, which allows tuning their optical, electronic, magnetic and catalytic properties. This vast library of anisotropic particulate building blocks provides a powerful arsenal for engineering the assembly of specific targeted structures and systems.;Autonomous motion is distinctive from Brownian motion. Platinum half-coated Janus particles undergo self-propelled motion, which is induced by the catalytic decomposition of hydrogen peroxide. The average speed of the self-propelled Pt-SiO2 Janus particles increases with increasing the concentration of hydrogen peroxide. Motion direction analyses show that the probability for the Janus particles continuing to travel in nearly same direction goes higher in higher concentrations of hydrogen peroxide. Microscopic observation of the particle motion demonstrates that these Janus particles move, on average, with the platinum-coated region oriented opposite to the direction of motion. The trajectories of the autonomous motion exhibit a directed motion at short time scale but with an overall random behavior at long time scales. Huge benefit can be garnered by taking advantage of the self-propulsion component in the system. The control of the motion of the magnetic Janus particles in solutions of hydrogen peroxide is demonstrated using the external magnetic field. The magnetic Janus particles orient themselves with the equatorial plane parallel to the applied field and the motion direction is perpendicular to the field. The directed motion has a more distinct preferred direction compared to the case in the absence of magnetic field, and the applied field is verified to control the orientation, not influence the speed of the particle motion.;Anisotropic particles are unique building blocks to assemble complex structures. The surface functionalized Janus particles with alkanethiols are adsorbed at the interfaces of liquid-air and liquid-liquid, forming monolayers with metal hemispheres pointing to the same direction. By changing the liquid oil phase, the orientation of the Janus particles can be manipulated, which provides an opportunity to selectively modify the surface in either phase. The preferential orientation in the same direction at interfaces allows for direct transfer of the Janus particles while the desired faces remain in either a face-down or face-up configuration. An external intervention, magnetic field, is also sought to direct the assembly of the magnetic Janus particles. In the presence of uniform magnetic field, the magnetic Janus particles form staggered chain structures with the chain direction parallel to the direction of the applied field. These chain structures are destroyed due to the capillary force during solvent evaporation. However, these soft structures are successfully locked in place after the solution dries by the addition of ammonium carbonate to the solution, which suggests a promising way to achieve 2D or 3D super structures for the fabrication of photonic crystals and photonic devices