3,089 research outputs found
Randomly Charged Polymers, Random Walks, and Their Extremal Properties
Motivated by an investigation of ground state properties of randomly charged
polymers, we discuss the size distribution of the largest Q-segments (segments
with total charge Q) in such N-mers. Upon mapping the charge sequence to
one--dimensional random walks (RWs), this corresponds to finding the
probability for the largest segment with total displacement Q in an N-step RW
to have length L. Using analytical, exact enumeration, and Monte Carlo methods,
we reveal the complex structure of the probability distribution in the large N
limit. In particular, the size of the longest neutral segment has a
distribution with a square-root singularity at l=L/N=1, an essential
singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near
l=1 is related to a another interesting RW problem which we call the "staircase
problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
The Phase Diagram of Crystalline Surfaces
We report the status of a high-statistics Monte Carlo simulation of
non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of
size up to nodes. We impose free boundary conditions. The free energy
is a gaussian spring tethering potential together with a normal-normal bending
energy. Particular emphasis is given to the behavior of the model in the cold
phase where we measure the decay of the normal-normal correlation function.Comment: 9 pages latex (epsf), 4 EPS figures, uuencoded and compressed.
Contribution to Lattice '9
Synergetic modelling of the Russian Federation’s energy system parameters
The energy system in any country is the basis of the whole economy. The level of its development largely determines the quantity and quality of economic entities, periods of economic growth, fall and stagnation. A high percentage of the power-deficient municipalities in the Russian Federation shows the substantive issues in this sphere that carries a threat to the energy security of the state. One of the promising trends for enhancing the energy security is the renewable energy sources (RES). Their use has the obvious benefits: it provides electricity to power-deficient and inaccessible areas, contributes to the introduction and spread of new technologies, thus solving the important social and economic problem. At that, it is important to determine the optimum ratio using of the recovery of renewable and conventional energy sources (CES). One of the main challenges in this regard is to build a model that adequately reflects the ratio of renewable and conventional energy sources in the Russian energy system. The paper presents the results of a synergistic approach to the construction of such a model. The Lotka- Volterra model was the main instrument used, which allowed to study a behavior pattern of the considered systems on the basis of the simplified regularities. It was found that the best possible qualitative “jump” in the Russian energy sector was in 2008. The calculations allowed to investigate the behavior of the Russian energy system with the variation of the initial conditions and to assess the validity of the targets for the share of electricity produced through the use of renewable energy in the total electric power of the country
Collapse of Randomly Self-Interacting Polymers
We use complete enumeration and Monte Carlo techniques to study
self--avoiding walks with random nearest--neighbor interactions described by
, where is a quenched sequence of ``charges'' on the
chain. For equal numbers of positive and negative charges (), the
polymer with undergoes a transition from self--avoiding behavior to a
compact state at a temperature . The collapse temperature
decreases with the asymmetry Comment: 8 pages, TeX, 4 uuencoded postscript figures, MIT-CMT-
A coding problem for pairs of subsets
Let be an --element finite set, an integer. Suppose that
and are pairs of disjoint -element subsets of
(that is, , , ). Define the distance of these pairs by . This is the
minimum number of elements of one has to move to obtain the other
pair . Let be the maximum size of a family of pairs of
disjoint subsets, such that the distance of any two pairs is at least .
Here we establish a conjecture of Brightwell and Katona concerning an
asymptotic formula for for are fixed and . Also,
we find the exact value of in an infinite number of cases, by using
special difference sets of integers. Finally, the questions discussed above are
put into a more general context and a number of coding theory type problems are
proposed.Comment: 11 pages (minor changes, and new citations added
Qualitative, comparative, and collaborative research at large scale: The GENNOVATE field methodology
Probability distributions for polymer translocation
We study the passage (translocation) of a self-avoiding polymer through a
membrane pore in two dimensions. In particular, we numerically measure the
probability distribution Q(T) of the translocation time T, and the distribution
P(s,t) of the translocation coordinate s at various times t. When scaled with
the mean translocation time , Q(T) becomes independent of polymer length,
and decays exponentially for large T. The probability P(s,t) is well described
by a Gaussian at short times, with a variance that grows sub-diffusively as
t^{\alpha} with \alpha~0.8. For times exceeding , P(s,t) of the polymers
that have not yet finished their translocation has a non-trivial stable shape.Comment: 5 pages, 4 figure
Ground States of Two-Dimensional Polyampholytes
We perform an exact enumeration study of polymers formed from a (quenched)
random sequence of charged monomers , restricted to a 2-dimensional
square lattice. Monomers interact via a logarithmic (Coulomb) interaction. We
study the ground state properties of the polymers as a function of their excess
charge for all possible charge sequences up to a polymer length N=18. We
find that the ground state of the neutral ensemble is compact and its energy
extensive and self-averaging. The addition of small excess charge causes an
expansion of the ground state with the monomer density depending only on .
In an annealed ensemble the ground state is fully stretched for any excess
charge .Comment: 6 pages, 6 eps figures, RevTex, Submitted to Phys. Rev.
Collineation group as a subgroup of the symmetric group
Let be the projectivization (i.e., the set of one-dimensional vector
subspaces) of a vector space of dimension over a field. Let be a
closed (in the pointwise convergence topology) subgroup of the permutation
group of the set . Suppose that contains the
projective group and an arbitrary self-bijection of transforming a
triple of collinear points to a non-collinear triple. It is well-known from
\cite{KantorMcDonough} that if is finite then contains the
alternating subgroup of .
We show in Theorem \ref{density} below that , if
is infinite.Comment: 9 page
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