38,005 research outputs found
Correlation function algebra for inhomogeneous fluids
We consider variational (density functional) models of fluids confined in
parallel-plate geometries (with walls situated in the planes z=0 and z=L
respectively) and focus on the structure of the pair correlation function
G(r_1,r_2). We show that for local variational models there exist two
non-trivial identities relating both the transverse Fourier transform G(z_\mu,
z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2
and z_3. These relations form an algebra which severely restricts the possible
form of the function G_0(z_\mu,z_\nu). For the common situations in which the
equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an
odd or even reflection symmetry in the z=L/2 plane the algebra simplifies
considerably and is used to relate the correlation function to the finite-size
excess free-energy \gamma(L). We rederive non-trivial scaling expressions for
the finite-size contribution to the free-energy at bulk criticality and for
systems where large scale interfacial fluctuations are present. Extensions to
non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte
Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site
Condensation occurs in nonequilibrium steady states when a finite fraction of
particles in the system occupies a single lattice site. We study condensation
transitions in a one-dimensional zero-range process with a single defect site.
The system is analysed in the grand canonical and canonical ensembles and the
two are contrasted. Two distinct condensation mechanisms are found in the grand
canonical ensemble. Discrepancies between the infinite and large but finite
systems' particle current versus particle density diagrams are investigated and
an explanation for how the finite current goes above a maximum value predicted
for infinite systems is found in the canonical ensemble.Comment: 18 pages, 4 figures, revtex
Effective anisotropies and energy barriers of magnetic nanoparticles with NĂ©el surface anisotropy
Magnetic nanoparticles with NĂ©el surface anisotropy, different internal structures, surface arrangements, and elongation are modeled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure, and shape. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects. (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) In symmetric particles (spherical and truncated octahedral) with cubic core anisotropy surface effects can change the sing of the latter. We also show that the competition between the core and surface anisotropies leads to a new energy that contributes to both the second- and fourth-order effective anisotropies. We evaluate energy barriers ÎE as functions of the strength of the surface anisotropy and the particle size. The results are analyzed with the help of the effective one-spin potential, which allows us to assess the consistency of the widely used formula ÎE/V= Kâ +6 Ks /D, where Kâ is the core anisotropy constant, Ks is a phenomenological constant related to surface anisotropy, and D is the particle's diameter. We show that the energy barriers are consistent with this formula only for elongated particles for which the surface contribution to the effective uniaxial anisotropy scales with the surface and is linear in the constant of the NĂ©el surface anisotropy. © 2007 The American Physical Society
Periodically driven stochastic un- and refolding transitions of biopolymers
Mechanical single molecule experiments probe the energy profile of
biomolecules. We show that in the case of a profile with two minima (like
folded/unfolded) periodic driving leads to a stochastic resonance-like
phenomenon. We demonstrate that the analysis of such data can be used to
extract four basic parameters of such a transition and discuss the statistical
requirements of the data acquisition. As advantages of the proposed scheme, a
polymeric linker is explicitly included and thermal fluctuations within each
well need not to be resolved.Comment: 7 pages, 5 figures, submitted to EP
Alternating steady state in one-dimensional flocking
We study flocking in one dimension, introducing a lattice model in which
particles can move either left or right. We find that the model exhibits a
continuous nonequilibrium phase transition from a condensed phase, in which a
single `flock' contains a finite fraction of the particles, to a homogeneous
phase; we study the transition using numerical finite-size scaling.
Surprisingly, in the condensed phase the steady state is alternating, with the
mean direction of motion of particles reversing stochastically on a timescale
proportional to the logarithm of the system size. We present a simple argument
to explain this logarithmic dependence. We argue that the reversals are
essential to the survival of the condensate. Thus, the discrete directional
symmetry is not spontaneously broken.Comment: 8 pages LaTeX2e, 5 figures. Uses epsfig and IOP style. Submitted to
J. Phys. A (Math. Gen.
Factorised Steady States in Mass Transport Models
We study a class of mass transport models where mass is transported in a
preferred direction around a one-dimensional periodic lattice and is globally
conserved. The model encompasses both discrete and continuous masses and
parallel and random sequential dynamics and includes models such as the
Zero-range process and Asymmetric random average process as special cases. We
derive a necessary and sufficient condition for the steady state to factorise,
which takes a rather simple form.Comment: 6 page
Spontaneous Jamming in One-Dimensional Systems
We study the phenomenon of jamming in driven diffusive systems. We introduce
a simple microscopic model in which jamming of a conserved driven species is
mediated by the presence of a non-conserved quantity, causing an effective long
range interaction of the driven species. We study the model analytically and
numerically, providing strong evidence that jamming occurs; however, this
proceeds via a strict phase transition (with spontaneous symmetry breaking)
only in a prescribed limit. Outside this limit, the nearby transition
(characterised by an essential singularity) induces sharp crossovers and
transient coarsening phenomena. We discuss the relevance of the model to two
physical situations: the clustering of buses, and the clogging of a suspension
forced along a pipe.Comment: 8 pages, 4 figures, uses epsfig. Submitted to Europhysics Letter
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