1,721,094 research outputs found
One-dimensional gas of hard needles
No full textWe study a one-dimensional gas of needlelike 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
Probability distributions for directed polymers in random media with correlated noise
No full textThe probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in d=1+1 dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent β, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.National Science Foundation (U.S.) (Grant No. DMR-12-06323)Massachusetts Institute of Technology (Thomas Frank Fellowship
Coalescence Model for Crumpled Globules Formed in Polymer Collapse
Full text linkThe rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived “crumpled globule.” The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not “equilibrate” subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting that the slow approach to scaling is related to the wide distribution of blob sizes.National Science Foundation (U.S.) (Grant DMR-12-06323)MIT Department of Physics Pappalardo Program (Fellowship
Localization of random walks to competing manifolds of distinct dimensions
No full textWe consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we consider a RW near a rectangular wedge in two dimensions, where the (zero-dimensional) corner and the (one-dimensional) wall have competing localization properties. This model applies also (as cross section) to an ideal polymer attracted to the surface or edge of a rectangular wedge in three dimensions. More generally, we consider (d−1)- and (d−2)-dimensional manifolds in d-dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multicritical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.National Science Foundation (U.S.) (Grant DMR-1708280)National Science Foundation (U.S.) (Grant PHY 1748958
Fluctuation-Induced Forces in Nonequilibrium Diffusive Dynamics
Full text linkFluctuations in nonequilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations, in turn, experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. Our model calculations show that the force falls off with slab separation d as k[subscript B]T/d (at temperature T, and in all spatial dimensions) but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is nonuniversal and explicitly depends on dynamics. The techniques introduced can be used to study pressure and fluctuation induced forces in a broad class of nonequilibrium systems.National Science Foundation (U.S.) (Grant DMR-12-06323
First-passage distributions in a collective model of anomalous diffusion with tunable exponent
No full textWe consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes whose friction coefficients scale as wave number to the power 2−z. A single (tagged) monomer then executes subdiffusion over a broad range of time scales, and its mean square displacement increases as t[superscript α] with α=1/z. To demonstrate nontrivial aspects of the model, we numerically study the absorption of the tagged particle in one dimension near an absorbing boundary or in the interval between two such boundaries. We obtain absorption probability densities as a function of time, as well as the position-dependent distribution for unabsorbed particles, at several values of α. Each of these properties has features characterized by exponents that depend on α. Characteristic distributions found for different values of α have similar qualitative features, but are not simply related quantitatively. Comparison of the motion of translocation coordinate of a polymer moving through a pore in a membrane with the diffusing tagged monomer with identical α also reveals quantitative differences
Universality in the jamming limit for elongated hard particles in one dimension
Full text linkWe study the thermodynamics properties of a one-dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in a two-dimensional space. Correlations between orientations of the objects are studied (by the 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.Israel Science Foundation (Grant No. 99/08)National Science Foundation (U.S.) (Grant No. DMR-08-03315)National Science Foundation (U.S.) (NSF Grant No. PHY05-51164
Equilibrium forces on nonreciprocal materials
No full textWe discuss and analyze the properties of Casimir forces acting between nonreciprocal objects in thermal equilibrium. By starting from the fluctuation-dissipation theorem and splitting the force into those arising from individual sources, we show that if all temperatures are equal, the resulting force is reciprocal and is derivable as the gradient of a Casimir (free) energy. While the expression for the free energy is identical to the one for reciprocal objects, there are several distinct features: To leading order in reflections, the free energy can be decomposed as the sum of two terms, the first corresponding to two reciprocal objects, and the second corresponding to two antireciprocal objects. The first term is negative and typically yields attraction, while the second can have either sign. For the case of two objects that are each other's mirror images, the second term is positive and yields repulsion. The sum of terms can lead to overall repulsive forces, in agreement with previous observations. Stable configurations, ruled out for reciprocal cases, appear possible for nonreciprocal objects. We show that for three objects, a three-body free energy exists, indicating that previously found persistent heat currents in situations of three objects cannot be used to produce persistent torques.National Science Foundation http://dx.doi.org/10.13039/10000000
Polymer-mediated entropic forces between scale-free objects
No full textThe number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines, or planes) the only relevant length scales are the polymer size R[subscript 0] and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h≪R[subscript 0], separation is the only remaining relevant scale and the entropic force must take the form F=Ak[subscript B]T/h. The amplitude A is universal and can be related to exponents η governing the anomalous scaling of polymer correlations in the presence of obstacles. We use analytical, numerical, and ε-expansion techniques to compute the exponent η for a polymer attached to the tip of the cone (with or without an additional plate or cone) for ideal and self-avoiding polymers. The entropic force is of the order of 0.1 pN at 0.1 μm for a single polymer and can be increased for a star polymer.National Science Foundation (U.S.) (Grant PHY05-51164)National Science Foundation (U.S.) (Grant DMR-12-06323
Attractive and repulsive polymer-mediated forces between scale-free surfaces
No full textWe consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation h between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals Ak_{B}T/h, where T is temperature. The amplitude A is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of A, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find A=0 for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).National Science Foundation (U.S.) (Grant DMR-1206323
- …
