1,789 research outputs found
Kinetic Anomalies in Addition-Aggregation Processes
We investigate irreversible aggregation in which monomer-monomer,
monomer-cluster, and cluster-cluster reactions occur with constant but distinct
rates K_{MM}, K_{MC}, and K_{CC}, respectively. The dynamics crucially depends
on the ratio gamma=K_{CC}/K_{MC} and secondarily on epsilon=K_{MM}/K_{MC}. For
epsilon=0 and gamma<2, there is conventional scaling in the long-time limit,
with a single mass scale that grows linearly in time. For gamma >= 2, there is
unusual behavior in which the concentration of clusters of mass k, c_k decays
as a stretched exponential in time within a boundary layer k<k* propto
t^{1-2/gamma} (k* propto ln t for gamma=2), while c_k propto t^{-2} in the bulk
region k>k*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma
>= 2.Comment: 6 pages, 2 column revtex4 format, for submission to J. Phys.
The nucleation behavior of supercooled water vapor in helium
The nucleation behavior of supersaturated water vapor in helium is experimentally investigated in the temperature range of 200–240 K. The experiments are performed using a pulse expansion wave tube. The experimental results show a sharp transition in the nucleation rates at 207 K. We suggest that the transition is due to the transition of vapor/liquid to vapor/solid nucleation (ordered with decreasing temperature). A qualitative theoretical explanation is given based on the classical nucleation theory and the surface energy of ice
Nontrivial Polydispersity Exponents in Aggregation Models
We consider the scaling solutions of Smoluchowski's equation of irreversible
aggregation, for a non gelling collision kernel. The scaling mass distribution
f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now,
only be computed by numerical simulations. We develop here new general methods
to obtain exact bounds and good approximations of . For the specific
kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles
moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R
is the particle radius), perturbative and nonperturbative expansions are
derived.
For a general kernel, we find exact inequalities for tau and develop a
variational approximation which is used to carry out the first systematic study
of tau(d,D) for KdD. The agreement is excellent both with the expansions we
derived and with existing numerical values. Finally, we discuss a possible
application to 2d decaying turbulence.Comment: 16 pages (multicol.sty), 6 eps figures (uses epsfig), Minor
corrections. Notations improved, as published in Phys. Rev. E 55, 546
Symmetry breaking in the Hubbard model at weak coupling
The phase diagram of the Hubbard model is studied at weak coupling in two and
three spatial dimensions. It is shown that the Neel temperature and the order
parameter in d=3 are smaller than the Hartree-Fock predictions by a factor of
q=0.2599. For d=2 we show that the self-consistent (sc) perturbation series
bears no relevance to the behavior of the exact solution of the Hubbard model
in the symmetry-broken phase. We also investigate an anisotropic model and show
that the coupling between planes is essential for the validity of
mean-field-type order parameters
Dynamical Cluster Approximation Employing FLEX as a Cluster Solver
We employ the Dynamical Cluster Approximation (DCA) in conjunction with the
Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA
is a technique to systematically restore the momentum conservation at the
internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field
Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which
classes of Feynman diagrams are summed over analytically using geometric
series. The FLEX is used as a tool to investigate the complementarity of the
DCA and the finite size lattice technique with periodic boundary conditions by
comparing their results for the Hubbard model. We also study the microscopic
theory underlying the DCA in terms of compact (skeletal) and non-compact
diagrammatic contributions to the thermodynamic potential independent of a
specific model. The significant advantages of the DCA implementation in
momentum space suggests the development of the same formalism for the frequency
space. However, we show that such a formalism for the Matsubara frequencies at
finite temperatures leads to acausal results and is not viable. However, a real
frequency approach is shown to be feasible.Comment: 15 pages, 24 figures. Submitted to Physical Review B as a Regular
Articl
Charge-order transition in the extended Hubbard model on a two-leg ladder
We investigate the charge-order transition at zero temperature in a two-leg
Hubbard ladder with additional nearest-neighbor Coulomb repulsion V using the
Density Matrix Renormalization Group technique. We consider electron densities
between quarter and half filling. For quarter filling and U=8t, we find
evidence for a continuous phase transition between a homogeneous state at small
V and a broken-symmetry state with "checkerboard" [wavevector Q=(pi,pi)] charge
order at large V. This transition to a checkerboard charge-ordered state
remains present at all larger fillings, but becomes discontinuous at
sufficiently large filling. We discuss the influence of U/t on the transition
and estimate the position of the tricritical points.Comment: 4 pages, 5 figs, minor changes, accepted for publication in PRB R
Removal of biofilms by impinging water droplets
The process of impinging water droplets on Streptococcus mutans biofilms was studied experimentally and numerically. Droplets were experimentally produced by natural breakup of a cylindrical liquid jet. Droplet diameter and velocity were varied between 20 and 200¿µm and between 20 and 100 m/s, respectively. The resulting erosion process of the biofilm was determined experimentally with high-speed recording techniques and a quantitative relationship between the removal rate, droplet size, and velocity was determined. The shear stress and the pressure on the surface during droplet impact were determined by numerical simulations, and a qualitative agreement between the experiment and the simulation was obtained. Furthermore, it was shown that the stresses on the surface are strongly reduced when a water film is present
Toward a systematic 1/d expansion: Two particle properties
We present a procedure to calculate 1/d corrections to the two-particle
properties around the infinite dimensional dynamical mean field limit. Our
method is based on a modified version of the scheme of Ref.
onlinecite{SchillerIngersent}}. To test our method we study the Hubbard model
at half filling within the fluctuation exchange approximation (FLEX), a
selfconsistent generalization of iterative perturbation theory. Apart from the
inherent unstabilities of FLEX, our method is stable and results in causal
solutions. We find that 1/d corrections to the local approximation are
relatively small in the Hubbard model.Comment: 4 pages, 4 eps figures, REVTe
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