1,151 research outputs found
Minimal Dynamical Triangulations of Random Surfaces
We introduce and investigate numerically a minimal class of dynamical
triangulations of two-dimensional gravity on the sphere in which only vertices
of order five, six or seven are permitted. We show firstly that this
restriction of the local coordination number, or equivalently intrinsic scalar
curvature, leaves intact the fractal structure characteristic of generic
dynamically triangulated random surfaces. Furthermore the Ising model coupled
to minimal two-dimensional gravity still possesses a continuous phase
transition. The critical exponents of this transition correspond to the usual
KPZ exponents associated with coupling a central charge c=1/2 model to
two-dimensional gravity.Comment: Latex, 9 pages, 3 figures, Published versio
Multicellular rosettes drive fluid-solid transition in epithelial tissues
Models for confluent biological tissues often describe the network formed by
cells as a triple-junction network, similar to foams. However, higher order
vertices or multicellular rosettes are prevalent in developmental and {\it in
vitro} processes and have been recognized as crucial in many important aspects
of morphogenesis, disease, and physiology. In this work, we study the influence
of rosettes on the mechanics of a confluent tissue. We find that the existence
of rosettes in a tissue can greatly influence its rigidity. Using a generalized
vertex model and effective medium theory we find a fluid-to-solid transition
driven by rosette density and intracellular tensions. This transition exhibits
several hallmarks of a second-order phase transition such as a growing
correlation length and a universal critical scaling in the vicinity a critical
point. Further, we elucidate the nature of rigidity transitions in dense
biological tissues and other cellular structures using a generalized Maxwell
constraint counting approach. This answers a long-standing puzzle of the origin
of solidity in these systems.Comment: 11 pages, 5 figures + 8 pages, 7 figures in Appendix. To be appear in
PR
Lecture Notes of Tensor Network Contractions
Tensor network (TN), a young mathematical tool of high vitality and great
potential, has been undergoing extremely rapid developments in the last two
decades, gaining tremendous success in condensed matter physics, atomic
physics, quantum information science, statistical physics, and so on. In this
lecture notes, we focus on the contraction algorithms of TN as well as some of
the applications to the simulations of quantum many-body systems. Starting from
basic concepts and definitions, we first explain the relations between TN and
physical problems, including the TN representations of classical partition
functions, quantum many-body states (by matrix product state, tree TN, and
projected entangled pair state), time evolution simulations, etc. These
problems, which are challenging to solve, can be transformed to TN contraction
problems. We present then several paradigm algorithms based on the ideas of the
numerical renormalization group and/or boundary states, including density
matrix renormalization group, time-evolving block decimation,
coarse-graining/corner tensor renormalization group, and several distinguished
variational algorithms. Finally, we revisit the TN approaches from the
perspective of multi-linear algebra (also known as tensor algebra or tensor
decompositions) and quantum simulation. Despite the apparent differences in the
ideas and strategies of different TN algorithms, we aim at revealing the
underlying relations and resemblances in order to present a systematic picture
to understand the TN contraction approaches.Comment: 134 pages, 68 figures. In this version, the manuscript has been
changed into the format of book; new sections about tensor network and
quantum circuits have been adde
Controllability and observability of grid graphs via reduction and symmetries
In this paper we investigate the controllability and observability properties
of a family of linear dynamical systems, whose structure is induced by the
Laplacian of a grid graph. This analysis is motivated by several applications
in network control and estimation, quantum computation and discretization of
partial differential equations. Specifically, we characterize the structure of
the grid eigenvectors by means of suitable decompositions of the graph. For
each eigenvalue, based on its multiplicity and on suitable symmetries of the
corresponding eigenvectors, we provide necessary and sufficient conditions to
characterize all and only the nodes from which the induced dynamical system is
controllable (observable). We discuss the proposed criteria and show, through
suitable examples, how such criteria reduce the complexity of the
controllability (respectively observability) analysis of the grid
A micro-accelerometer MDO benchmark problem
Many optimization and coordination methods for multidisciplinary design optimization (MDO) have been proposed in the last three decades. Suitable MDO benchmark problems for testing and comparing these methods are few however. This article presents a new MDO benchmark problem based on the design optimization of an ADXL150 type lateral capacitive micro-accelerometer. The behavioral models describe structural and dynamic effects, as well as electrostatic and amplification circuit contributions. Models for important performance indicators such as sensitivity, range, noise, and footprint area are presented. Geometric and functional constraints are included in these models to enforce proper functioning of the device. The developed models are analytical, and therefore highly suitable for benchmark and educational purposes. Four different problem decompositions are suggested for four design cases, each of which can be used for testing MDO coordination algorithms. As a reference, results for an all-in-one implementation, and a number of augmented Lagrangian coordination algorithms are given. © 2009 The Author(s)
Spectrum optimization in multi-user multi-carrier systems with iterative convex and nonconvex approximation methods
Several practical multi-user multi-carrier communication systems are
characterized by a multi-carrier interference channel system model where the
interference is treated as noise. For these systems, spectrum optimization is a
promising means to mitigate interference. This however corresponds to a
challenging nonconvex optimization problem. Existing iterative convex
approximation (ICA) methods consist in solving a series of improving convex
approximations and are typically implemented in a per-user iterative approach.
However they do not take this typical iterative implementation into account in
their design. This paper proposes a novel class of iterative approximation
methods that focuses explicitly on the per-user iterative implementation, which
allows to relax the problem significantly, dropping joint convexity and even
convexity requirements for the approximations. A systematic design framework is
proposed to construct instances of this novel class, where several new
iterative approximation methods are developed with improved per-user convex and
nonconvex approximations that are both tighter and simpler to solve (in
closed-form). As a result, these novel methods display a much faster
convergence speed and require a significantly lower computational cost.
Furthermore, a majority of the proposed methods can tackle the issue of getting
stuck in bad locally optimal solutions, and hence improve solution quality
compared to existing ICA methods.Comment: 33 pages, 7 figures. This work has been submitted for possible
publicatio
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