arXiv subjects

Yang Jiao

Publications and source records attributed to Yang Jiao.

159 records · Page 9Linked to original sources

arXiv2012

Rigidity of spherical codes

A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configuration of the Coxeter-Todd lattice is not jammed, despite being locally jammed (each individual cap is held in place if its neighbors are fixed); in this respect, the Coxeter-Todd lattice is analogous to the face-centered cubic lattice in three dimensions. By contrast, we find that many other packings have jammed kissing configurations, including the Barnes-Wall lattice and all of the best kissing configurations known in four through twelve dimensions. Jamming seems to become much less common for large kissing configurations in higher dimensions, and in particular it fails for the best kissing configurations known in 25 through 31 dimensions. Motivated by this phenomenon, we find new kissing configurations in these dimensions, which improve on the records set in 1982 by the laminated lattices.

math.MG↗

arXiv2012

Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient $D_e$ and mean survival time $τ$) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function $P(δ)$ for the networks and present a variety of analytical estimates of the effective diffusion coefficient $D_e$ for finite-sized diffusing particles. The Hashin-Strikman upper bound on the effective diffusion coefficient $D_e$ and the pore-size lower bound on the mean survival time $τ$ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient $D_e$ as well as the mean survival time $τ$, which is related to nuclear magnetic resonance (NMR) relaxation times. Specifically, the Torquato approximation provides the most accurate estimates of $D_e$ for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for $τ$ for the networks at different collagen concentrations. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here.

physics.bio-ph↗

arXiv2012

Density of States for a Specified Correlation Function and the Energy Landscape

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.

cond-mat.stat-mech↗

arXiv2012

Diversity of Dynamics and Morphologies of Invasive Solid Tumors

Complex tumor-host interactions can significantly affect the growth dynamics and morphologies of progressing neoplasms. The growth of a confined solid tumor induces mechanical pressure and deformation of the surrounding microenvironment, which in turn influences tumor growth. In this paper, we generalize a recently developed cellular automaton model for invasive tumor growth in heterogeneous microenvironments [Y. Jiao and S. Torquato, PLoS Comput. Biol. 7, e1002314 (2011)] by incorporating the effects of pressure. Specifically, we explicitly model the pressure exerted on the growing tumor due to the deformation of the microenvironment and its effect on the local tumor-host interface instability. Both noninvasive-proliferative growth and invasive growth with individual cells that detach themselves from the primary tumor and migrate into the surrounding microenvironment are investigated. We find that while noninvasive tumors growing in "soft" homogeneous microenvironments develop almost isotropic shapes, both high pressure and host heterogeneity can strongly enhance malignant behavior, leading to finger-like protrusions of the tumor surface. Moreover, we show that individual invasive cells of an invasive tumor degrade the local extracellular matrix at the tumor-host interface, which diminishes the fingering growth of the primary tumor. The implications of our results for cancer diagnosis, prognosis and therapy are discussed.

physics.bio-ph↗

arXiv2012

Emergent Behaviors from A Cellular Automaton Model for Invasive Tumor Growth in Heterogeneous Microenvironments

Understanding tumor invasion and metastasis is of crucial importance for both fundamental cancer research and clinical practice. In vitro experiments have established that the invasive growth of malignant tumors is characterized by the dendritic invasive branches composed of chains of tumor cells emanating from the primary tumor mass. The preponderance of previous tumor simulations focused on non-invasive (or proliferative) growth. The formation of the invasive cell chains and their interactions with the primary tumor mass and host microenvironment are not well understood. Here, we present a novel cellular automaton (CA) model that enables one to efficiently simulate invasive tumor growth in a heterogeneous host microenvironment. By taking into account a variety of microscopic-scale tumor-host interactions, including the short-range mechanical interactions between tumor cells and tumor stroma, degradation of extracellular matrix by the invasive cells and oxygen/nutrient gradient driven cell motions, our CA model predicts a rich spectrum of growth dynamics and emergent behaviors of invasive tumors. Besides robustly reproducing the salient features of dendritic invasive growth, such as least resistance and intrabranch homotype attraction, we also predict nontrivial coupling of the growth dynamics of the primary tumor mass and the invasive cells. In addition, we show that the properties of the host microenvironment can significantly affect tumor morphology and growth dynamics, emphasizing the importance of understanding the tumor-host interaction. The capability of our CA model suggests that well-developed in silico tools could eventually be utilized in clinical situations to predict neoplastic progression and propose individualized optimal treatment strategies.

physics.bio-ph↗

arXiv2012

A Superior Descriptor of Random Textures and Its Predictive Capacity

Two-phase random textures abound in a host of contexts, porous and composite media, ecological structures, biological media and astrophysical structures. Questions surrounding the spatial structure of such textures continue to pose many theoretical challenges. For example, can two-point correlation functions be identified that can be both manageably measured and yet reflect nontrivial higher-order structural information about the textures? We present a novel solution to this question by probing the information content of the widest class of different types of two-point functions examined to date using inverse "reconstruction" techniques. This enables us to show that a superior descriptor is the two-point cluster function $C_2({\bf r})$, which is sensitive to topological {\it connectedness} information. We demonstrate the utility of $C_2({\bf r})$ by accurately reconstructing textures drawn from materials science, cosmology and granular media, among other examples. Our work suggests an entirely new theoretical pathway to predict the bulk physical properties of random textures, and also has important ramifications for atomic and molecular systems.

cond-mat.mtrl-sci↗

arXiv2011

Analytical Construction of A Dense Packing of Truncated Tetrahedra

Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists mathematicians for centuries. Recently, organizing principles for the types of structures associated with the densest polyhedron packings have been put forth. However, finding the maximally dense packings for specific shapes remains nontrivial and is a subject of intensive research. Here, we analytically construct the densest known packing of truncated tetrahedra with $ϕ=207/208=0.995~192...$, which is amazingly close to unity and strongly implies that this packing is maximally dense. This construction is based on a generalized organizing principle for polyhedra that lack central symmetry. Moreover, we find that the holes in this putative optimal packing are small regular tetrahedra, leading to a new tiling of space by regular tetrahedra and truncated tetrahedra. We also numerically study the equilibrium melting properties of what apparently is the densest packing of truncated tetrahedra as the system undergoes decompression. Our simulations reveal two different stable crystal phases, one at high densities and the other at intermediate densities, as well as a first-order liquid-crystal phase transition.

cond-mat.soft↗

arXiv2011

Phase diagram and structural diversity of the densest binary sphere packings

The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the alpha-x plane of sphere radius ratio alpha and relative concentration x are at the Kepler limit alpha = 1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (alpha,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings.

cond-mat.stat-mech↗

arXiv2011

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales. Previous work on maximally random strictly jammed sphere packings in three dimensions has shown that these systems are hyperuniform and possess unusual quasi-long-range pair correlations, resulting in anomalous logarithmic growth in the number variance. However, recent work on maximally random jammed sphere packings with a size distribution has suggested that such quasi-long-range correlations and hyperuniformity are not universal among jammed hard-particle systems. In this paper we show that such systems are indeed hyperuniform with signature quasi-long-range correlations by characterizing the more general local-volume-fraction fluctuations. We argue that the regularity of the void space induced by the constraints of saturation and strict jamming overcomes the local inhomogeneity of the disk centers to induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic behavior in the spectral density, resulting in quasi-long-range spatial correlations. A numerical and analytical analysis of the pore-size distribution for a binary MRJ system in addition to a local characterization of the n-particle loops governing the void space surrounding the inclusions is presented in support of our argument. This paper is the first part of a series of two papers considering the relationships among hyperuniformity, jamming, and regularity of the void space in hard-particle packings.

cond-mat.stat-mech↗

arXiv2011

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape

We extend the results from the first part of this series of two papers by examining hyperuniformity in heterogeneous media composed of impenetrable anisotropic inclusions. Specifically, we consider maximally random jammed packings of hard ellipses and superdisks and show that these systems both possess vanishing infinite-wavelength local-volume-fraction fluctuations and quasi-long-range pair correlations. Our results suggest a strong generalization of a conjecture by Torquato and Stillinger [Phys. Rev. E. 68, 041113 (2003)], namely that all strictly jammed saturated packings of hard particles, including those with size- and shape-distributions, are hyperuniform with signature quasi-long-range correlations. We show that our arguments concerning the constrained distribution of the void space in MRJ packings directly extend to hard ellipse and superdisk packings, thereby providing a direct structural explanation for the appearance of hyperuniformity and quasi-long-range correlations in these systems. Additionally, we examine general heterogeneous media with anisotropic inclusions and show for the first time that one can decorate a periodic point pattern to obtain a hard-particle system that is not hyperuniform with respect to local-volume-fraction fluctuations. This apparent discrepancy can also be rationalized by appealing to the irregular distribution of the void space arising from the anisotropic shapes of the particles. Our work suggests the intriguing possibility that the MRJ states of hard particles share certain universal features independent of the local properties of the packings, including the packing fraction and average contact number per particle.

cond-mat.stat-mech↗

arXiv2011

Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings

We show that quasi-long-range (QLR) pair correlations that decay asymptotically with scaling $r^{-(d+1)}$ in $d$-dimensional Euclidean space $\mathbb{R}^d$, trademarks of certain quantum systems and cosmological structures, are a universal signature of maximally random jammed (MRJ) hard-particle packings. We introduce a novel hyperuniformity descriptor in MRJ packings by studying local-volume-fraction fluctuations and show that infinite-wavelength fluctuations vanish even for packings with size- and shape-distributions. Special void statistics induce hyperuniformity and QLR pair correlations.

cond-mat.stat-mech↗

arXiv2011

Non-Universality of Density and Disorder in Jammed Sphere Packings

We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with packing density $ϕ$ as low as 0.6. This is well below the value of 0.64 associated with the maximally random jammed state and entirely unrelated to the ill-defined ``random loose packing'' state density. Specifically, collectively jammed packings are generated with a very narrow distribution centered at any density $ϕ$ over a wide density range $ϕ\in [0.6,~0.74048\ldots]$ with variable disorder. Our results support the view that there is no universal jamming point that is distinguishable based on the packing density and frequency of occurence. Our jammed packings are mapped onto a density-order-metric plane, which provides a broader characterization of packings than density alone. Other packing characteristics, such as the pair correlation function, average contact number and fraction of rattlers are quantified and discussed.

cond-mat.stat-mech↗

arXiv2010

Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming

We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in $d$-dimensional Euclidean space $\mathbb{R}^d$, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential linear programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in $\mathbb{R}^d$ for $d=2,3,4,5$ and $6$ with a diversity of disorder and densities up to the maximally densities. This deterministic algorithm can produce a broad range of inherent structures besides the usual disordered ones with very small computational cost by tuning the radius of the {\it influence sphere}. In three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range $[0.6, 0.7408...]$. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for $d=2,3, 4,5$ and 6. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust and computationally faster at generating maximally dense packings, especially as the space dimension increases.

cond-mat.stat-mech↗

arXiv2010

Geometrical Ambiguity of Pair Statistics. II. Heterogeneous Media

In a previous paper [Jiao, Stillinger and Torquato, PRE 81, 011105 (2010)], we considered the geometrical ambiguity of pair statistics associated with point configurations. Here we focus on the analogous problem for heterogeneous media (materials). The complex structures of heterogeneous media are usually characterized via statistical descriptors, such as the $n$-point correlation function $S_n$. An intricate inverse problem of practical importance is to what extent a medium can be reconstructed from the two-point correlation function $S_2$ of a target medium. Recently, general claims of the uniqueness of reconstructions using $S_2$ have been made based on numerical studies. Here, we provide a systematic approach to characterize the geometrical ambiguity of $S_2$ for both continuous two-phase heterogeneous media and their digitized representations in a mathematically precise way. In particular, we derive the exact conditions for the case where two distinct media possess identical $S_2$. The degeneracy conditions are given in terms of integral and algebraic equations for continuous media and their digitized representations, respectively. By examining these equations and constructing their rigorous solutions for specific examples, we conclusively show that in general $S_2$ is indeed not sufficient information to uniquely determine the structure of the medium, which is consistent with the results of our recent study on heterogeneous media reconstruction [Jiao, Stillinger and Torquato, PNAS 106, 17634 (2009)]. The uniqueness issue of multiphase media reconstructions and additional structural information required to characterize heterogeneous media are discussed.

cond-mat.stat-mech↗

arXiv2009

Optimal Packings of Superballs

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a versatile family of convex particles (p >= 0.5) with both cubic- and octahedral-like shapes as well as concave particles (0 < p < 0.5) with octahedral-like shapes. In this paper, we provide analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings. The maximal packing density as a function of p is nonanalytic at the sphere-point (p = 1) and increases dramatically as p moves away from unity. The packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two-dimensional "superdisk" counterparts, and are distinctly different from that of ellipsoid packings. Our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems, which should deepen our understanding of the statistical thermodynamics of nonspherical-particle systems.

cond-mat.soft↗