Results 1  10
of
12
Global Order From Local Sources
 Bull. Amer. Math. Soc
, 1991
"... This article contains introductions to three open problems of significant research interest, taken from number theory, logic, and condensed matter physics. All three problems will be shown to have at their core special cases of one simplystated optimization problem. Our goal is to use the intuition ..."
Abstract

Cited by 31 (11 self)
 Add to MetaCart
This article contains introductions to three open problems of significant research interest, taken from number theory, logic, and condensed matter physics. All three problems will be shown to have at their core special cases of one simplystated optimization problem. Our goal is to use the intuition gained from these three perspectives to direct attention to this common core, which constitutes, in fact, one problem of remarkable depth and importance. We will also show that some of the tools developed in the separate problems are of real value in the others. Since each of the three problems uses jargon peculiar to its field, we will give an informal introduction to each, together with all relevant definitions, in the following section. However it may be useful to include here a very brief description of each of them to give some idea of our eventual goal. Our first problem is "sphere packing", in which we consider arrangements of infinitely many unit diameter spheres, each sphere having a variable position in R
Thermodynamics and Garbage Collection
 In ACM Sigplan Notices
, 1994
"... INTRODUCTION Computer scientists should have a knowledge of abstract statistical thermodynamics. First, computer systems are dynamical systems, much like physical systems, and therefore an important first step in their characterization is in finding properties and parameters that are constant over ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
INTRODUCTION Computer scientists should have a knowledge of abstract statistical thermodynamics. First, computer systems are dynamical systems, much like physical systems, and therefore an important first step in their characterization is in finding properties and parameters that are constant over time (i.e., constants of motion). Second, statistical thermodynamics successfully reduces macroscopic properties of a system to the statistical behavior of large numbers of microscopic processes. As computer systems become large assemblages of small components, an explanation of their macroscopic behavior may also be obtained as the aggregate statistical behavior of its component parts. If not, the elegance of the statistical thermodynamical approach can at least provide inspiration for new classes of models. 1 Third, the components of computer systems are approaching the same size as the microscopic pr
Evolution in the information age: rediscovering the nature of the organism
"... The newest synthesis of evolutionary thought is emerging, and promises to return evolutionary biology to Darwin’s panoramic view of life. The key element is a longstanding dualism in evolutionary theory. This dualism has a long history within evolutionary biology, being manifested under guises such ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
The newest synthesis of evolutionary thought is emerging, and promises to return evolutionary biology to Darwin’s panoramic view of life. The key element is a longstanding dualism in evolutionary theory. This dualism has a long history within evolutionary biology, being manifested under guises such as: (1) the nature of the organism and the nature of the conditions, (2) internal and external, or intrinsic and extrinsic, factors, (3) production and exchanges, (4) boundary and initial conditions, (5) metabolism and replication, (6) energy and information, and (7) costs and benefits, and conflict and resolution. A partially retrospective review suggests that there is now a conceptual coherent framework for resolving the dualism, not by eliminating one component of the dualism but by integrating both.
An Ultimate Frustration in Classical LatticeGas Models
, 1997
"... . We compare tiling systems with squarelike tiles and classical latticegas models with translationinvariant, finiterange interactions between particles. For a given tiling, there is a natural construction of a corresponding latticegas model. With oneto one correspondence between particles and ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
. We compare tiling systems with squarelike tiles and classical latticegas models with translationinvariant, finiterange interactions between particles. For a given tiling, there is a natural construction of a corresponding latticegas model. With oneto one correspondence between particles and tiles, we simply assign a positive energy to pairs of nearestneighbor particles which do not match as tiles; otherwise the energy of interaction is zero. Such models of interacting particles are called nonfrustrated  all interactions can attain their minima simultaneously. Groundstate configurations of these models correspond to tilings; they have the minimal energy density equal to zero. There are frustrated latticegas models; antiferromagnetic Ising model on the triangular lattice is a standard example. However, in all such models known so far, one could always find a nonfrustrated interaction having the same groundstate configurations. Here we constructed an uncountable family of cla...
Stable Quasicrystalline Ground States
, 1997
"... . We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice gas models with translationinvariant finite range interactions and with ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice gas models with translationinvariant finite range interactions and with unique quasiperiodic ground states which are stable against small perturbations of finite range potentials. 1 Introduction One of the important problems in physics is to understand why matter is crystalline at low temperatures [1, 2, 3, 4, 5, 6, 7]. It is traditionally assumed (but has never been proved) that at zero temperature minimization of the free energy of a system of many interacting particles can only be obtained by their periodic arrangements (a perfect crystal) which at nonzero temperature is disrupted by defects due to entropy. Recently, however, there has been a growing evidence, that this basic phenomenon, the crystalline symmetry of low temperature matter, has exceptions; ...
An Argument Against the Unification Account of Explanation
, 1999
"... This paper argues that an increase in the known unifying power of a theory is often not accompanied in an increase the perceived quality of its explanations. The theory may explain many new things, but it does not explain the old things any better just because it now explains the new things. This s ..."
Abstract
 Add to MetaCart
This paper argues that an increase in the known unifying power of a theory is often not accompanied in an increase the perceived quality of its explanations. The theory may explain many new things, but it does not explain the old things any better just because it now explains the new things. This strongly suggests that unification accounts of explanation are mistaken. I conclude with a discussion of the explanatory role of unification in science. A surprising consequence of the discussion is that unification has explanatory role only in a nonHumean world, a world with real causal powers and laws of nature. 1
The Conceptual Role of ‘Temperature ’ in Statistical Mechanics: Or How Probabilistic Averages Maximize Predictive Accuracy*
"... helpful discussions on previous drafts and related topics. ABSTRACT: If scientific reduction requires that microtheories explain the truth of macrotheories, then reduction appears to be an unfulfilled goal of science even in the best examples. If reduction is viewed more liberally as requiring only ..."
Abstract
 Add to MetaCart
helpful discussions on previous drafts and related topics. ABSTRACT: If scientific reduction requires that microtheories explain the truth of macrotheories, then reduction appears to be an unfulfilled goal of science even in the best examples. If reduction is viewed more liberally as requiring only that the microtheory explains the predictive accuracy of macrotheories, then there may be real examples of reduction. 2 1
Viscosity from Newton to Nonequilibrium Statistical Mechanics ∗
, 2006
"... This paper is devoted to the transport process of momentum, the viscosity. We outline the historical development of hydrodynamics, the branch of physics in which the shear and bulk viscosities are expressed. We show the transition between the mechanical philosophy claiming that the conservation of e ..."
Abstract
 Add to MetaCart
This paper is devoted to the transport process of momentum, the viscosity. We outline the historical development of hydrodynamics, the branch of physics in which the shear and bulk viscosities are expressed. We show the transition between the mechanical philosophy claiming that the conservation of energy is coupled to cyclic, reversible dynamics, and the birth of a new science, thermodynamics, in which the conservation of energy (the first law) is associated with the irreversibility (the second law). Through the 19th century, the kinetic theory of gases was developed and accumulated successes establishing relationships between the microscopic dynamics of the atoms and molecules, and macroscopic properties, among which the viscosity. In this context appeared the paradox of irreversibility to which Boltzmann was the first to provide an explanation based on a statistical interpretation of the entropy. We finally outline the history of the theory of chaos and show how the chaotic character of the microscopic dynamics provides a dynamical explanation of the irreversible processes such as transport, and in particular, the viscosity. In this context, we present three successfull approaches developed the last two decades: the thermostatedsystem method, the escaperate formalism and the hydrodynamicmode method. This paper consists in a revision of the introduction of the PhD thesis presented
Stable Quasicrystalline Ground States
, 2008
"... Abstract. We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice gas models with translationinvariant, finiterange interactions ..."
Abstract
 Add to MetaCart
Abstract. We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice gas models with translationinvariant, finiterange interactions and with a unique quasiperiodic ground state which is stable against small perturbations of twobody potentials. More generally, we provide a criterion for stability of nonperiodic ground states. Key words: Quasicrystals, nonperiodic tilings, classical lattice gas models, ground states, stability.