arXiv subjects

Yacov Kantor

Publications and source records attributed to Yacov Kantor.

At least 37 records · Page 2Linked to original sources

arXiv2009

Universality in the jamming limit for elongated hard particles in one dimension

We study thermodynamics properties of a one dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in two-dimensional space. Correlations between orientations of the objects are studied (by transfer matrix method) as a function of density and aspect ratio. The behavior in the extreme high-density (jamming) limit is described by a few universality classes depending on the object's shape. In particular, there is a diverging correlation length when the contact point of adjacent objects is far from the line along which their centers move, as for needles and rectangles.

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arXiv2009

One-dimensional gas of hard needles

We study a one dimensional gas of needle-like objects as a testing ground for a formalism that relates the thermodynamic properties of "hard" potentials to the probabilities for contacts between particles. Specifically, we use Monte Carlo methods to calculate the pressure and elasticity coefficient of the hard-needle gas as a function of its density. The results are then compared to the same quantities obtained analytically from a transfer matrix approach.

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arXiv2008

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^α with α~0.8. For times exceeding , P(s,t) of the polymers that have not yet finished their translocation has a non-trivial stable shape.

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arXiv2007

Anomalous Diffusion with Absorbing Boundary

In a very long Gaussian polymer on time scales shorter that the maximal relaxation time, the mean squared distance travelled by a tagged monomer grows as ~t^{1/2}. We analyze such sub-diffusive behavior in the presence of one or two absorbing boundaries and demonstrate the differences between this process and the sub-diffusion described by the fractional Fokker-Planck equation. In particular, we show that the mean absorption time of diffuser between two absorbing boundaries is finite. Our results restrict the form of the effective dispersion equation that may describe such sub-diffusive processes.

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arXiv2006

Elasticity of a system with non-central potentials

We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via non-central two-body potentials as thermal averages of products of first and second partial derivatives of the interparticle potentials and components of the interparticle separation vectors. These results are adapted to hard potentials, when the stress and the elastic constants are expressed as thermal averages of the components of normals to contact surfaces between the particles and components of vectors separating the centers of the particles. The averages require the knowledge of simultaneous contact probabilities of two pairs of particles. We apply the expressions to particles for which a contact function can be defined, and demonstrate the feasibility of the method by computing the stress and the elastic constants of a two-dimensional system of hard ellipses using Monte Carlo simulations.

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arXiv2004

Apex Exponents for Polymer--Probe Interactions

We consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents $γ_1$ and $γ_2$, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, vary continuously with the tip's angle. These apex exponents are calculated analytically by $ε$-expansion, and numerically by simulations in three dimensions. We find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.

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arXiv2003

Anomalous Dynamics of Forced Translocation

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N^2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (sub-diffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N^2 and N^{1+ν}, respectively, where νis the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).

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arXiv2003

Tight and loose shapes in flat entangled dense polymers

We investigate the effects of topological constraints (entanglements) on two dimensional polymer loops in the dense phase, and at the collapse transition (Theta point). Previous studies have shown that in the dilute phase the entangled region becomes tight, and is thus localised on a small portion of the polymer. We find that the entropic force favouring tightness is considerably weaker in dense polymers. While the simple figure-eight structure, created by a single crossing in the polymer loop, localises weakly, the trefoil knot and all other prime knots are loosely spread out over the entire chain. In both the dense and Theta conditions, the uncontracted knot configuration is the most likely shape within a scaling analysis. By contrast, a strongly localised figure-eight is the most likely shape for dilute prime knots. Our findings are compared to recent simulations.

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arXiv2003

Entropic competition between knots and slip-links

Using canonical Monte Carlo simulations, we introduce a new numerical procedure for comparing the entropic exponents of polymers with different constraints and/or topologies. Setting up competitions between polymer segments which can exchange monomers according to their free energies, we obtain the universal exponents of partition functions, independently of any knowledge of the non-universal part. The method is successfully tested for closed polymer loops decorated with sliding rings. We also investigate the entropic exponents of loops with a fixed knot type, in which case we are limited by strong finite--size effects.

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arXiv2003

Knot Probability for Self-Avoiding Loops on a Cubic Lattice

We investigate the probability for appearance of knots in self-avoiding loops (SALs) on a cubic lattice. A set of N-step loops is generated by attempting to combine pairs of (N/2)-step self-avoiding walks constructed by a dimerization method. We demonstrate that our method produces unbiased samples of SALs, and study the knot formation probability as a function of loop size. Our results corroborate the conclusions of Yao et. al. with loops generated by a Monte Carlo method.

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arXiv2002

Knots in Charged Polymers

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.

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arXiv2002

Force-Extension Relations for Polymers with Sliding Links

Topological entanglements in polymers are mimicked by sliding rings (slip-links) which enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip-links create additional loops of variable size. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation: The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus--de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.

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arXiv2002

Pulling Knotted Polymers

We compare Monte Carlo simulations of knotted and unknotted polymers whose ends are connected to two parallel walls. The force $f$ exerted on the polymer is measured as a function of the separation $R$ between the walls. For unknotted polymers of several monomer numbers $N$, the product $fN^ν$ is a simple function of $R/N^ν$, where $ν\simeq 0.59$. By contrast, knotted polymers exhibit strong finite size effects which can be interpreted in terms of a new length scale related to the size of the knot. Based on this interpretation, we conclude that the number of monomers forming the knot scales as $N^t$, with $t=0.4\pm 0.1$.

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arXiv2002

Tightness of slip-linked polymer chains

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops which can exchange length between each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip-links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.

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arXiv2001

Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.

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arXiv2001

Anomalous Dynamics of Translocation

We study the dynamics of the passage of a polymer through a membrane pore (translocation), focusing on the scaling properties with the number of monomers $N$. The natural coordinate for translocation is the number of monomers on one side of the hole at a given time. Commonly used models which assume Brownian dynamics for this variable predict a mean (unforced) passage time $τ$ that scales as $N^2$, even in the presence of an entropic barrier. However, the time it takes for a free polymer to diffuse a distance of the order of its radius by Rouse dynamics scales with an exponent larger than 2, and this should provide a lower bound to the translocation time. To resolve this discrepancy, we perform numerical simulations with Rouse dynamics for both phantom (in space dimensions $d=1$ and 2), and self-avoiding (in $d=2$) chains. The results indicate that for large $N$, translocation times scale in the same manner as diffusion times, but with a larger prefactor that depends on the size of the hole. Such scaling implies anomalous dynamics for the translocation process. In particular, the fluctuations in the monomer number at the hole are predicted to be non-diffusive at short times, while the average pulling velocity of the polymer in the presence of a chemical potential difference is predicted to depend on $N$.

cond-mat.soft↗

arXiv2001

Entropic Elasticity at the Sol-Gel Transition

The sol-gel transition is studied in two purely entropic models consisting of hard spheres in continuous three-dimensional space, with a fraction $p$ of nearest neighbor spheres tethered by inextensible bonds. When all the tethers are present ($p=1$) the two systems have connectivities of simple cubic and face-centered cubic lattices. For all $p$ above the percolation threshold $p_c$, the elasticity has a cubic symmetry characterized by two distinct shear moduli. When $p$ approaches $p_c$, both shear moduli decay as $(p-p_c)^f$, where $f\simeq 2$ for each type of the connectivity. This result is similar to the behavior of the conductivity in random resistor networks, and is consistent with many experimental studies of gel elasticity. The difference between the shear moduli that measures the deviation from isotropy decays as $(p-p_c)^h$, with $h\simeq 4$.

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arXiv2000

Entropic Elasticity of Phantom Percolation Networks

A new method is used to measure the stress and elastic constants of purely entropic phantom networks, in which a fraction $p$ of neighbors are tethered by inextensible bonds. We find that close to the percolation threshold $p_c$ the shear modulus behaves as $(p-p_c)^f$, where the exponent $f\approx 1.35$ in two dimensions, and $f\approx 1.95$ in three dimensions, close to the corresponding values of the conductivity exponent in random resistor networks. The components of the stiffness tensor (elastic constants) of the spanning cluster follow a power law $\sim(p-p_c)^g$, with an exponent $g\approx 2.0$ and 2.6 in two and three dimensions, respectively.

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