Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions.

With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane y>0 with different boundary conditions a and b on the negative and positive x axes. For ab=-+ and f+, they determined the one- and two-point averages of the spin σ and energy ε. Here +,-, and f stand for spin-up, spin-down, and free-spin boundaries, respectively.

Casimir interaction of rodlike particles in a two-dimensional critical system.

We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus.

Fluctuations of a long, semiflexible polymer in a narrow channel.

We consider an inextensible, semiflexible polymer or wormlike chain, with persistence length P and contour length L, fluctuating in a cylindrical channel of diameter D. In the regime D< occupied by the polymer and the mean-square deviation from the average vary as =[1-α(∘)(D/P)(2/3)]L and <ΔR(∥)(2)>=β(∘)(D(2)P)L , respectively, where α(∘) and β(∘) are dimensionless amplitudes. In earlier work we determined α(∘) and the analogous amplitude α(square) for a channel with a rectangular cross section from simulations of very long chains.

Extreme statistics for time series: distribution of the maximum relative to the initial value.

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/falpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRHI).

Free energy and extension of a semiflexible polymer in cylindrical confining geometries.

We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D< View Article and Find Full Text PDF

Equilibrium statistics of an inelastically bouncing ball, subject to gravity and a random force.

We consider a particle moving on the half line x > 0 and subject to a constant force in the -x direction plus a delta-correlated random force. At x = 0 the particle is reflected inelastically. The velocities just after and before the reflection satisfy v(f) = -r v(i), where r is the coefficient of restitution.

Randomly accelerated particle in a box: mean absorption time for partially absorbing and inelastic boundaries.

Consider a particle which is randomly accelerated by Gaussian white noise on the line segment 0 View Article and Find Full Text PDF

Helical polymer in cylindrical confining geometries.

Using an algorithm for simulating equilibrium configurations, we study a fluctuating helical polymer either (i) contained in a cylindrical pore or (ii) wound around a cylindrical rod. We work in the regime where both the contour length and the persistence length of the helical polymer are much larger than the diameter of the cylinder. In case (i) we calculate the free energy of confinement and interpret it in terms of a wormlike chain in a pore with an effective diameter that depends on the parameters of the helix.

Equilibrium of a confined, randomly accelerated, inelastic particle: is there inelastic collapse?

We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 0 View Article and Find Full Text PDF

Free energy of a long, flexible, self-avoiding polymer chain in a tube.

The confinement free energy of a long, flexible, self-avoiding polymer chain, fluctuating in d spatial dimensions in an infinitely long cylindrical tube with diameter L, is given by DeltaF approximately Ak(B)TL(-1)R(parallel) for R(parallel)>>L. Here R(parallel) is the length of tube occupied by the chain, and A is a universal amplitude. We show how to determine DeltaF and R(parallel) from the correlation length xi(L)(t) of the n-vector model of magnetism in the limit n-->0, defined on the cylindrical volume, near the critical temperature t(c)(L) where xi(L) diverges.

Semiflexible polymer in a uniform force field in two dimensions.

The conformational properties of a semiflexible polymer chain, anchored at one end in a uniform force field, are studied in a simple two-dimensional model. Recursion relations are derived for the partition function and then iterated numerically. We calculate the angular fluctuations of the polymer about the direction of the force field and the average polymer configuration as functions of the bending rigidity, chain length, chain orientation at the anchoring point, and field strength.

Dynamics of inelastic collapse.

We consider a particle randomly accelerated by Gaussian white noise on the half-line x>0. The collisions of the particle with the wall at x=0 are inelastic. The velocities just before and after reflection are related by v(f)=-rv(i), where r is the coefficient of restitution.