1,320 research outputs found
Rigorous Non-Perturbative Ornstein-Zernike Theory for Ising Ferromagnets
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation
functions for finite-range Ising ferromagnets in any dimensions and at any
temperature above critical
Solution of the Percus-Yevick equation for hard discs
We solve the Percus-Yevick equation in two dimensions by reducing it to a set
of simple integral equations. We numerically obtain both the pair correlation
function and the equation of state for a hard disc fluid and find good
agreement with available Monte-Carlo calculations. The present method of
resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure
Evolution of collision numbers for a chaotic gas dynamics
We put forward a conjecture of recurrence for a gas of hard spheres that
collide elastically in a finite volume. The dynamics consists of a sequence of
instantaneous binary collisions. We study how the numbers of collisions of
different pairs of particles grow as functions of time. We observe that these
numbers can be represented as a time-integral of a function on the phase space.
Assuming the results of the ergodic theory apply, we describe the evolution of
the numbers by an effective Langevin dynamics. We use the facts that hold for
these dynamics with probability one, in order to establish properties of a
single trajectory of the system. We find that for any triplet of particles
there will be an infinite sequence of moments of time, when the numbers of
collisions of all three different pairs of the triplet will be equal. Moreover,
any value of difference of collision numbers of pairs in the triplet will
repeat indefinitely. On the other hand, for larger number of pairs there is but
a finite number of repetitions. Thus the ergodic theory produces a limitation
on the dynamics.Comment: 4 pages, published versio
The Effect of Direct to Consumer Television Advertising on the Timing of Treatment
We examine how direct to consumer advertising (DCA) affects the delay between diagnosis and pharmacological treatment for patients suffering from a common chronic disease. The primary data for this study consist of patients diagnosed with osteoarthritis (N=18,235) taken from a geographically diverse national research network of 72 primary care practices with 348 physicians in 27 states over the 1999 to 2002 time period. Brand specific advertising data was collected for local and network television at the monthly-level for the nearest media markets to the practices. Results of duration models of delay to treatment suggest advertising does affect the length of time that patients and physicians wait to initiate therapy. This evidence suggests these effects may be welfare enhancing, in that advertising tends to encourage more rapid adoption among patients who are good clinical candidates for the therapy, and leads to less rapid adoption among some patients who are poor clinical candidates.Health and Safety, Technology and Industry
Orbit equivalence rigidity for ergodic actions of the mapping class group
We establish orbit equivalence rigidity for any ergodic, essentially free and
measure-preserving action on a standard Borel space with a finite positive
measure of the mapping class group for a compact orientable surface with higher
complexity. We prove similar rigidity results for a finite direct product of
mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove
Quantum criticality around metal-insulator transitions of strongly correlated electrons
Quantum criticality of metal-insulator transitions in correlated electron
systems is shownto belong to an unconventional universality class with
violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry
breaking transitions. This unconventionality arises from an emergent character
of the quantum critical point, which appears at the marginal point between the
Ising-type symmetry breaking at nonzero temperatures and the topological
transition of the Fermi surface at zero temperature. We show that Hartree-Fock
approximations of an extended Hubbard model on square latticesare capable of
such metal-insulator transitions with unusual criticality under a preexisting
symmetry breaking. The obtained universality is consistent with the scaling
theory formulated for Mott transition and with a number of numerical results
beyond the mean-field level, implying that the preexisting symmetry breaking is
not necessarily required for the emergence of this unconventional universality.
Examinations of fluctuation effects indicate that the obtained critical
exponents remain essentially exact beyond the mean-field level. Detailed
analyses on the criticality, containing diverging carrier density fluctuations
around the marginal quantum critical point, are presented from microscopic
calculations and reveal the nature as quantum critical "opalescence". Analyses
on crossovers between GLW type at nonzero temperature and topological type at
zero temperature show that the critical exponents observed in (V,Cr)2O3 and
kappa-ET-type organic conductor provide us with evidences for the existence of
the present marginal quantum criticality.Comment: 24 pages, 19 figure
Change in Quality of Life after a Cancer Diagnosis among a Nationally Representative Cohort of Older Adults in the US
Scale-free networks as preasymptotic regimes of superlinear preferential attachment
We study the following paradox associated with networks growing according to
superlinear preferential attachment: superlinear preference cannot produce
scale-free networks in the thermodynamic limit, but there are superlinearly
growing network models that perfectly match the structure of some real
scale-free networks, such as the Internet. We obtain an analytic solution,
supported by extensive simulations, for the degree distribution in
superlinearly growing networks with arbitrary average degree, and confirm that
in the true thermodynamic limit these networks are indeed degenerate, i.e.,
almost all nodes have low degrees. We then show that superlinear growth has
vast preasymptotic regimes whose depths depend both on the average degree in
the network and on how superlinear the preference kernel is. We demonstrate
that a superlinearly growing network model can reproduce, in its preasymptotic
regime, the structure of a real network, if the model captures some
sufficiently strong structural constraints -- rich-club connectivity, for
example. These findings suggest that real scale-free networks of finite size
may exist in preasymptotic regimes of network evolution processes that lead to
degenerate network formations in the thermodynamic limit
Structure and aggregation of colloids immersed in critical solvents
We consider an ensemble of spherical colloidal particles immersed in a
near-critical solvent such as a binary liquid mixture close to its critical
demixing point. The emerging long-ranged fluctuations of the corresponding
order parameter of the solvent drive the divergence of the correlation length.
Spatial confinements of these critical fluctuations by colloidal solute
particles, acting as cavities in the fluctuating medium, restrict and modify
the fluctuation spectrum in a way which depends on their relative
configuration. This results in effective, so-called critical Casimir forces
(CCFs) acting on the confining surfaces. Using the available knowledge about
CCFs we study the structure and stability of such colloidal suspensions by
employing an approach in terms of effective, one-component colloidal systems.
Applying the approximation of pairwise additive CCFs we calculate the radial
distribution function of the colloids, which is experimentally accessible. We
analyze colloidal aggregation due to CCFs and thus allude to previous
experimental studies which are still under debat
Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions
We solve the Percus-Yevick equation in even dimensions by reducing it to a
set of simple integro-differential equations. This work generalizes an approach
we developed previously for hard discs. We numerically obtain both the pair
correlation function and the virial coefficients for a fluid of hyper-spheres
in dimensions and 8, and find good agreement with available exact
results and Monte-Carlo simulations. This paper confirms the alternating
character of the virial series for , and provides the first evidence
for an alternating character for . Moreover, we show that this sign
alternation is due to the existence of a branch point on the negative real
axis. It is this branch point that determines the radius of convergence of the
virial series, whose value we determine explicitly for . Our results
complement, and are consistent with, a recent study in odd dimensions [R.D.
Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)].Comment: Accepted for publication in J. Chem. Phys. (11 pages, 6 figures
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