1,180 research outputs found
A lattice gas of prime numbers and the Riemann Hypothesis
In recent years, there has been some interest in applying ideas and methods
taken from Physics in order to approach several challenging mathematical
problems, particularly the Riemann Hypothesis. Most of these kind of
contributions are suggested by some quantum statistical physics problems or by
questions originated in chaos theory. In this letter we show that the real part
of the non-trivial zeros of the Riemann zeta function extremizes the grand
potential corresponding to a simple model of one-dimensional classical lattice
gas, the critical point being located at 1/2 as the Riemann Hypothesis claims.Comment: 12 page
Free energies as invariants of Teichmüller like structures
A Teichmüller like structure on the space of d-degree holomorphic maps on the circle S1, marked by conjugations to the map z 7→ z d, can be defined. Here we introduce a definition of free energy associated to this kind of dynamics as an invariant of equivalence classes in the Teichmüller space. This quantity encodes a length spectrum of rotation cycles in S1.Fil: Meson, Alejandro Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería; Argentin
Partial Differential Equations as Three-Dimensional Inverse Problem of Moments
We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E= (a1, b1)x(a2, b2)x(a3, b3). We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.Fil: Pintarelli, María Beatriz. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin
Bounds for Estimators of Ergodic Averages
We consider different ergodic averages and estimate the measure of the set of points in which the averages apart from a given value. The cases considered are empirical measures of cylinders in symbolic spaces and averages of maps given a kind Lyapunov exponents, in a such spaces. Besides we obtain bounds for the fluctuations of ergodic averages from amenable action groups. The bounds obtained are valid for any ¨time¨, not only, like in case of large deviations, for asymptotic values.Fil: Meson, Alejandro Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin
On the topological entropy of the irregular part of v-statistics multifractal spectra
Let (x, d) be a compact metric space and f : x → x, if xr is the product of r−copies of x, r ≥ 1, and φ : xr → r, then the multifractal decomposition for v −statistics is given by eφ (α) = ( x : lim n→∞ 1 nr p 0≤i1≤...≤ir≤n−1 φ ¡ f i1 (x) , ..., fir (x) ¢ = α ) . The irregular part, or historic set, of the spectrum is the set points x ∈ x, for which the limit does not exist. In this article we prove that for dynamical systems with specification, the irregular part of the v −statistics spectrum has topological entropy equal to that of the whole space x.Fil: Meson, Alejandro Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin
Convergence of the barycentre of measures from Fuchsian action groups
We prove the pointwise ergodic convergence of the sequence of barycentres of empirical measures which are defined from the action of Fuchsian groups and by maps valuated in CAT(0)−spaces. A result of this nature was established by Austin from actions of amenable groups and defining the empirical measures from Følner sequences. Here we de- fine different sequences of barycentres, in particular we do not consider a topological structure on the group and Følner sequences.Fil: Meson, Alejandro Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Vericat, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin
New criteria for cluster identification in continuum systems
Two new criteria, that involve the microscopic dynamics of the system, are
proposed for the identification of clusters in continuum systems. The first one
considers a residence time in the definition of the bond between pairs of
particles, whereas the second one uses a life time in the definition of an
aggregate. Because of the qualitative features of the clusters yielded by the
criteria we call them chemical and physical clusters, respectively. Molecular
dynamics results for a Lennard-Jones system and general connectivity theories
are presented.Comment: 31 pages, 11 figures, The following article has been accepted by The
Journal of Chemical Physics. After it is published, it will be found at
http://ojps.aip.org/jcpo
Chirality in a quaternionic representation of the genetic code
A quaternionic representation of the genetic code, previously reported by the
authors, is updated in order to incorporate chirality of nucleotide bases and
amino acids. The original representation assigns to each nucleotide base a
prime integer quaternion of norm 7 and involves a function that associates with
each codon, represented by three of these quaternions, another integer
quaternion (amino acid type quaternion) in such a way that the essentials of
the standard genetic code (particulaty its degeneration) are preserved. To show
the advantages of such a quaternionic representation we have, in turn,
associated with each amino acid of a given protein, besides of the type
quaternion, another real one according to its order along the protein (order
quaternion) and have designed an algorithm to go from the primary to the
tertiary structure of the protein by using type and order quaternions. In this
context, we incorporate chirality in our representation by observing that the
set of eight integer quaternions of norm 7 can be partitioned into a pair of
subsets of cardinality four each with their elements mutually conjugates and by
putting they in correspondence one to one with the two sets of enantiomers (D
and L) of the four nucleotide bases adenine, cytosine, guanine and uracil,
respectively. Thus, guided by two diagrams proposed for the codes evolution, we
define functions that in each case assign a L- (D-) amino acid type integer
quaternion to the triplets of D- (L-) bases. The assignation is such that for a
given D-amino acid, the associated integer quaternion is the conjugate of that
one corresponding to the enantiomer L. The chiral type quaternions obtained for
the amino acids are used, together with a common set of order quaternions, to
describe the folding of the two classes, L and D, of homochiral proteins.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1505.0465
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