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The Arithmetic Symmetry of Multilattices: Another View on the 29 Types of Monoatomic 2Lattices
"... This paper studies the ensuing arithmetic classification in the simplest threedimensional case, that is, monoatomic 2lattices (triply periodic structures with two indistinguishable points in their unit cell). We show that there exist 29 distinct arithmetic types of monoatomic 2lattices. As all mo ..."
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This paper studies the ensuing arithmetic classification in the simplest threedimensional case, that is, monoatomic 2lattices (triply periodic structures with two indistinguishable points in their unit cell). We show that there exist 29 distinct arithmetic types of monoatomic 2lattices. As all monoatomic 2lattices are constituted by a single crystallographic orbit, these structures are also classified by the established criterion of Fischer and Koch (1975, 1996); the two classifications coincide. Among the 29 types we retrieve the 5 Strukturberichte that are themselves monoatomic 2lattices, which indicates how many more such structures there exist in theory (to compare, recall that the arithmetic types of 1lattices are the classical 14 Bravais types, among which 6 are listed as Strukturberichte) . 1. Introduction 1.1. Background
Symmetry breaking in monoatomic 2lattices
"... In this paper we describe all the possibilities for symmetry breaking transformations in monoatomic 2lattices (crystal structures with two identical points in their unit translational cell). This is done by establishing the symmetry hierarchies (partial ordering) for the arithmetic classes of symme ..."
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In this paper we describe all the possibilities for symmetry breaking transformations in monoatomic 2lattices (crystal structures with two identical points in their unit translational cell). This is done by establishing the symmetry hierarchies (partial ordering) for the arithmetic classes of symmetry groups of these crystals (Fig. 1). We also study the ‘EricksenPitteri neighbourhoods ’ for them, thus making a local analysis of their configuration space. We give details about two physically relevant cases, analysing the neighbourhoods and the possible symmetrybreaking mechanisms for the diamond and the hexagonal closepacked structures (Figs. 2 and 3). 1
Critical Exponents and Renormalization
, 1998
"... This paper deals with the theory of critical exponents and whether and how these exponents can be influenced if one includes disorder in a given pure system. Moreover, the renormalization group flow is examined in a more general framework. The paper itself consists of three parts. In the first part ..."
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This paper deals with the theory of critical exponents and whether and how these exponents can be influenced if one includes disorder in a given pure system. Moreover, the renormalization group flow is examined in a more general framework. The paper itself consists of three parts. In the first part the wellknown results for the Ising system, given by renormalization, are reviewed. After the introduction of the basic concepts and definitions of phase transitions and phenomenological Landau theory, an expression for the Landau free energy of the Ising system is derived. Once this result is obtained, the correspondence to the O(N) symmetric OE
Planelike minimizers in periodic media: jet flows and
 University of Texas at Austin
, 2001
"... This paper is divided in three parts. In the first part, we consider the functional a i,j (x) # i u # j u + Q(x) # (1,1) (u) dx , for a i,j and Q periodic under integer translations. We assume that Q is bounded and bounded away from zero, and a i,j is a bounded elliptic matrix. We prove that t ..."
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This paper is divided in three parts. In the first part, we consider the functional a i,j (x) # i u # j u + Q(x) # (1,1) (u) dx , for a i,j and Q periodic under integer translations. We assume that Q is bounded and bounded away from zero, and a i,j is a bounded elliptic matrix. We prove that there exists a universal constant M 0 , depending only on n, the bounds on a i,j and Q stated above, such that: given any # , there exists a class A minimizer u for the functional #]}.
http://www.fzjuelich.de/nicseries/volume20 Accessing the Dynamics of StronglyCorrelated Many Body Systems within the Operator Loop Update and its Application to HighTemperature Superconductivity
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— Cosmic strings in a swimming pool.
, 2004
"... Abstract: A new dynamical bifurcation mechanism finally explains the formation of topological defects experimentally observed and defined in 1986 as Falaco Solitons. The Falaco Solitons are topologically universal phenomena created experimentally by a macroscopic rotational dynamics in a continuous ..."
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Abstract: A new dynamical bifurcation mechanism finally explains the formation of topological defects experimentally observed and defined in 1986 as Falaco Solitons. The Falaco Solitons are topologically universal phenomena created experimentally by a macroscopic rotational dynamics in a continuous media with a discontinuity surface, such as that found in a swimming pool. The topologically coherent structure of Falaco Solitons replicates certain features found at all physical scales, from spiral arm galaxies and cosmic strings to microscopic hadrons. The easy to replicate experiment indicates the creation of "stationary " thermodynamic states (or solitons) far from equilibrium, which are locally unstable but are globally stabilized. Several exact solutions to the NavierStokes equations are demonstrated to admit bifurcations to Falaco Solitons. It is conjectured that the universal coherent topological features of the Falaco Solitons can appear as cosmological realizations of Wheeler’s wormholes, could represent spin pairing mechanisms in the microscopic Fermi surface, and exhibit the confinement problem of sub microscopic quarks on the end of a string, or are perhaps realizations of subsubmicroscopic strings connecting branes.
Fluidodinamica: i nuovi aspetti
"... Sommario: I problemi della teoria del moto dei fluidi sono ben illustrati nel caso dei fluidi viscosi incomprimibili: la teoria della nascita della turbolenza ha subito un rivolgimento nel XX secolo divenendo per qualche lustro il centro di indagini teoriche e sperimentali. Pur non avendo ancora rag ..."
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Sommario: I problemi della teoria del moto dei fluidi sono ben illustrati nel caso dei fluidi viscosi incomprimibili: la teoria della nascita della turbolenza ha subito un rivolgimento nel XX secolo divenendo per qualche lustro il centro di indagini teoriche e sperimentali. Pur non avendo ancora raggiunto una sistemazione teorica soddisfacente lasciano ormai nuovamente il posto a ricerche sulla turbolenza sviluppata e la sua relazione con i fenomeni caotici. 1 Fluidi e loro modelli “Fluida ” è ogni sostanza che può assumere la forma del suo contenitore senza che sia necessario compiere lavoro. Quindi, in condizioni normali, l’acqua, il vapore, l’aria, l’alcool sono fluidi. I fluidi sono esempi di “continui”: e prima dell’affermazione dell’atomismo, definitiva solo un secolo fa, erano considerati infinitamente divisibili, come pure ogni altra forma di materia (quali i solidi o i vetri). Anzi il vuoto stesso era considerato non esistente e, quindi, come una sostanza continua anche se non visibile. Gli studi di Archimede, Stevino, Torricelli, Bernoulli portarono a stabilire le equazioni che reggono i moti dei fluidi ideali, ossia non viscosi, e non. Con le equazioni ebbero inizio la fluidodinamica teorica moderna e le sue applicazioni più avanzate, dalle previsioni meteorologiche, alla progettazione di profili alari, allo studio delle correnti marine. Eulero ottenne, 250 anni fa, le equazioni per un fluido ideale immaginando di decomporlo in parti assai piccole; ciascuna occupante un “elemento di volume ” v con densità ρ (e quindi massa m = ρ v) ed assimilabile a un punto materiale soggetto alle leggi della dinamica newtoniana: l’elemento di volume situato nel punto generico x interno al contenitore ha dunque una
Distributions of Knots and Links in Circular DNA
"... The distinctive feature of closed circular molecules is that they occupy particular topological states that cannot be altered by any conformational rearrangement short of breaking DNA strands. This topological constraint opens unique possibilities for experimental studies of the distributions of top ..."
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The distinctive feature of closed circular molecules is that they occupy particular topological states that cannot be altered by any conformational rearrangement short of breaking DNA strands. This topological constraint opens unique possibilities for experimental studies of the distributions of topological states created by different ways. Primarily, the equilibrium distributions of topological properties are considered in the review. We describe how such distributions can be obtained and measured experimentally and how they can be computed. Comparison of the calculated and measured equilibrium distributions of knots and links formed by circular molecules gave a lot of valuable information about properties of the double helix. Study of the steady state fraction of knots and links created by type II DNA topoisomerases exposed surprising property of the enzymes, their ability to reduce these fractions essentially below the equilibrium level. 1.
THE PHYSICS OF INFORMATION INFORMATION THEORY IN THE LIGHT OF THERMODYNAMICS, STATISTICAL MECHANICS AND NONLINEAR DYNAMICS
, 2005
"... 2.1. The laws 3 2.2. Free energy 6 ..."