arXiv subjects

Yacov Kantor

Publications and source records attributed to Yacov Kantor.

53 records · Page 3Linked to original sources

arXiv2000

Elasticity of Gaussian and nearly-Gaussian phantom networks

We study the elastic properties of phantom networks of Gaussian and nearly-Gaussian springs. We show that the stress tensor of a Gaussian network coincides with the conductivity tensor of an equivalent resistor network, while its elastic constants vanish. We use a perturbation theory to analyze the elastic behavior of networks of slightly non-Gaussian springs. We show that the elastic constants of phantom percolation networks of nearly-Gaussian springs have a power low dependence on the distance of the system from the percolation threshold, and derive bounds on the exponents.

cond-mat.stat-mech↗

arXiv2000

The Elastic Behavior of Entropic "Fisherman's Net"

A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the distance between them to a certain maximal separation, but having zero energy at all smaller lengths. We measure the elastic constants for many values of the ratio $γ$ between the maximal and actual extensions of the net. When the net is very stretched ($γ\sim 1$), a simple transformation maps the system into a triangular hard disks solid, and we show that the elastic properties of both systems, coincide. We also show that the crossover to a Gaussian elastic behavior, expected for the non-stressed net, occurs when the net is more loose ($γ\sim 3$).

cond-mat.stat-mech↗

arXiv1999

Loops in One Dimensional Random Walks

Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate numerically and analytically loops in several types of RWs, including RWs with continuous step-length distribution. We show that for long walks the probability density of the longest loop becomes independent of the details of the walks and definition of the loops. We investigate crossovers and convergence of probability densities to the limiting behavior, and obtain some of the analytical properties of the universal probability density.

cond-mat.soft↗

arXiv1998

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).

cond-mat.soft↗

arXiv1997

Ground States of Two-Dimensional Polyampholytes

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$, 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 $Q$ 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 $Q$. In an annealed ensemble the ground state is fully stretched for any excess charge $Q>0$.

cond-mat.soft↗

arXiv1997

Two-Dimensional Polymers with Random Short-Range Interactions

We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that a polymer undergoes a collapse transition at a temperature $T_θ$, which decreases with increasing imbalance between charges. At the transition point, the dependence of the radius of gyration of the polymer on the number of monomers is characterized by an exponent $ν_θ = 0.60 \pm 0.02$, which is slightly larger than the similar exponent for homopolymers. We find no evidence of freezing at low temperatures.

cond-mat.soft↗

arXiv1997

Pseudo-boundaries in discontinuous 2-dimensional maps

It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently smooth 2-dimensional area-preserving maps. When such boundaries are destroyed, they become pseudo-boundaries. We show that pseudo-boundaries can also be found in discontinuous maps. The origin of these pseudo-boundaries are groups of chains of islands which separate parts of the phase space and need to be crossed in order to move between the different sub-spaces. Trajectories, however, do not easily cross these chains, but tend to propagate along them. This type of behavior is demonstrated using a ``generalized'' Fermi map.

cond-mat.stat-mech↗

arXiv1996

Statistics of Largest Loops in a Random Walk

We report further findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor, Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional random walks (RWs), this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which exhibits an essential singularity. We establish analytical upper and lower bounds on the probability distribution, and numerically probe the distribution down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15}) using a recursive Monte Carlo algorithm. We also investigate the possibility of singularities at \ell=1/k for integer k.

cond-mat↗

arXiv1996

Conformations of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M< (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.

cond-mat↗

arXiv1996

Collapse of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This result is inconsistent with results obtained from free energy considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).

cond-mat↗

arXiv1995

Randomly Charged Polymers: Excess Charge Dependence of Spatial Configurations

Spatial configurations of randomly charged polymers, known as polyampholytes (PAs), are very sensitive to the overall excess charge Q. Analytical arguments, supported by Monte Carlo simulations and exact enumeration studies, lead to the following picture: For Q < Q_c = q_0 N^2 (q_0 is the elementary charge, N is the number of monomers in the polymer), the radius of gyration R_g of the polymer decreases with decreasing temperature T and the polymer becomes compact, while for Q>Q_c the polymer stretches with decreasing T. At low T, the dense states are described by Debye-Huckel theory, while the expanded states resemble a necklace of globules connected by strings. At such temperatures, the transition between the dense and the expanded states with increasing Q, is reminiscent of the breakup of a charged drop.

cond-mat↗

arXiv1995

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.

cond-mat↗

arXiv1995

Randomly Charged Polymers: An Exact Enumeration Study

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$. Such polymers, known as polyampholytes, are compact when completely neutral and expanded when highly charged. Our exhaustive search included all spatial conformations and quenched sequences for up to 12--step (13--site) walks. We investigate the behavior of the polymer as a function of its overall excess charge $Q$, and temperature $T$. At low temperatures there is a phase transition from compact to extended configurations when the charge exceeds $Q_c\approx q_0 \sqrt{N}$. There are also indications of a transition for small $Q$ between two compact states on varying temperature. Numerical estimates are provided for the condensation energy, surface tension, and the critical exponent $ν$.

cond-mat↗

arXiv1994

Instabilities of Charged Polyampholytes

We consider polymers formed from a (quenched) random sequence of charged monomers of opposite signs. Such polymers, known as polyampholytes (PAs), are compact when completely neutral and expanded when highly charged. We examine the transition between the two regimes by Monte Carlo simulations, and by analogies to charged drops. We find that the overall excess charge, $Q$, is the main determinant of the size of the PA. A polymer composed of $N$ charges of $\pm q_0$ is compact for $Q<Q_c\approx q_0 \sqrt{N}$, and expanded otherwise. The transition is reminiscent of the Rayleigh shape instability of a charged drop. A uniform excess charge causes the breakup of a fluid drop, and stretches out a polymer to a {\it necklace} shape. The inhomogeneities in charge distort the shape away from an ordered necklace.

cond-mat↗

arXiv1994

Extremal Segments in Random Sequences

We investigate the probability for the largest segment in with total displacement $Q$ in an $N$-step random walk 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 loop has a distribution with a square-root singularity at $\ell\equiv L/N=1$, an essential singularity at $\ell=0$, and a discontinuous derivative at $\ell=1/2$.

cond-mat↗

arXiv1994

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 $v_0q_iq_j$, where $q_i=\pm1$ is a quenched sequence of ``charges'' on the chain. For equal numbers of positive and negative charges ($N_+=N_-$), the polymer with $v_0>0$ undergoes a transition from self--avoiding behavior to a compact state at a temperature $θ\approx1.2v_0$. The collapse temperature $θ(x)$ decreases with the asymmetry $x=|N_+-N_-|/(N_++N_-)$

cond-mat↗

arXiv1994

Excess Charge in Polyampholytes

Polyampholytes (PAs) are polymers composed of (quenched) random sequences of positive and negatively charged monomeric groups. We show that the radius of gyration, $R_g$, of a PA strongly depends on its overall excess charge $Q$, and is very weakly influenced by other aspects of the sequence. For $Q Q_c$ it is stretched. Some aspects of this behavior can be understood by analogy with the shape instability of a charged drop where the Rayleigh charge plays the role of $Q_c$.

cond-mat↗