1,947 research outputs found
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
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
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 impact of loco-regional recurrences on metastatic progression in early-stage breast cancer: a multistate model
To study whether the effects of prognostic factors associated with the occurrence of distant metastases (DM) at primary diagnosis change after the incidence of loco-regional recurrences (LRR) among women treated for invasive stage I or II breast cancer. The study population consisted of 3,601 women, enrolled in EORTC trials 10801, 10854, or 10902 treated for early-stage breast cancer. Data were analysed in a multivariate, multistate model by using multivariate Cox regression models, including a state-dependent covariate. The presence of a LRR in itself is a significant prognostic risk factor (HR: 3.64; 95%-CI: 2.02-6.5) for the occurrence of DM. Main prognostic risk factors for a DM are young age at diagnosis (</=40: HR: 1.79; 95%-CI: 1.28-2.51), larger tumour size (HR: 1.58; 95%-CI: 1.35-1.84) and node positivity (HR: 2.00; 95%-CI: 1.74-2.30). Adjuvant chemotherapy is protective for a DM (HR: 0.66; 95%-CI: 0.55-0.80). After the occurrence of a LRR the latter protective effect has disappeared (P = 0.009). The presence of LRR in itself is a significant risk factor for DM. For patients who are at risk of developing LRR, effective local control should be the main target of therapy
Fluctuation-driven insulator-to-metal transition in an external magnetic field
We consider a model for a metal-insulator transition of correlated electrons
in an external magnetic field. We find a broad region in interaction and
magnetic field where metallic and insulating (fully magnetized) solutions
coexist and the system undergoes a first-order metal-insulator transition. A
global instability of the magnetically saturated solution precedes the local
ones and is caused by collective fluctuations due to poles in electron-hole
vertex functions.Comment: REVTeX 4 pages, 3 PS figure
Phase separation and the segregation principle in the infinite-U spinless Falicov-Kimball model
The simplest statistical-mechanical model of crystalline formation (or alloy
formation) that includes electronic degrees of freedom is solved exactly in the
limit of large spatial dimensions and infinite interaction strength. The
solutions contain both second-order phase transitions and first-order phase
transitions (that involve phase-separation or segregation) which are likely to
illustrate the basic physics behind the static charge-stripe ordering in
cuprate systems. In addition, we find the spinodal-decomposition temperature
satisfies an approximate scaling law.Comment: 19 pages and 10 figure
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
Temperature dependence of antiferromagnetic order in the Hubbard model
We suggest a method for an approximative solution of the two dimensional
Hubbard model close to half filling. It is based on partial bosonisation,
supplemented by an investigation of the functional renormalisation group flow.
The inclusion of both the fermionic and bosonic fluctuations leads in lowest
order to agreement with the Hartree-Fock result or Schwinger-Dyson equation and
cures the ambiguity of mean field theory . We compute the temperature
dependence of the antiferromagnetic order parameter and the gap below the
critical temperature. We argue that the Mermin-Wagner theorem is not
practically applicable for the spontaneous breaking of the continuous spin
symmetry in the antiferromagnetic state of the Hubbard model. The long distance
behavior close to and below the critical temperature is governed by the
renormalisation flow for the effective interactions of composite Goldstone
bosons and deviates strongly from the Hartree-Fock result.Comment: New section on critical behavior 31 pages,17 figure
A Survey of Numerical Solutions to the Coagulation Equation
We present the results of a systematic survey of numerical solutions to the
coagulation equation for a rate coefficient of the form A_ij \propto (i^mu j^nu
+ i^nu j^mu) and monodisperse initial conditions. The results confirm that
there are three classes of rate coefficients with qualitatively different
solutions. For nu \leq 1 and lambda = mu + nu \leq 1, the numerical solution
evolves in an orderly fashion and tends toward a self-similar solution at large
time t. The properties of the numerical solution in the scaling limit agree
with the analytic predictions of van Dongen and Ernst. In particular, for the
subset with mu > 0 and lambda < 1, we disagree with Krivitsky and find that the
scaling function approaches the analytically predicted power-law behavior at
small mass, but in a damped oscillatory fashion that was not known previously.
For nu \leq 1 and lambda > 1, the numerical solution tends toward a
self-similar solution as t approaches a finite time t_0. The mass spectrum n_k
develops at t_0 a power-law tail n_k \propto k^{-tau} at large mass that
violates mass conservation, and runaway growth/gelation is expected to start at
t_crit = t_0 in the limit the initial number of particles n_0 -> \infty. The
exponent tau is in general less than the analytic prediction (lambda + 3)/2,
and t_0 = K/[(lambda - 1) n_0 A_11] with K = 1--2 if lambda > 1.1. For nu > 1,
the behaviors of the numerical solution are similar to those found in a
previous paper by us. They strongly suggest that there are no self-consistent
solutions at any time and that runaway growth is instantaneous in the limit n_0
-> \infty. They also indicate that the time t_crit for the onset of runaway
growth decreases slowly toward zero with increasing n_0.Comment: 41 pages, including 14 figures; accepted for publication in J. Phys.
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