22,911 research outputs found
Mean Field Limits for Interacting Diffusions in a Two-Scale Potential
In this paper we study the combined mean field and homogenization limits for
a system of weakly interacting diffusions moving in a two-scale, locally
periodic confining potential, of the form considered
in~\cite{DuncanPavliotis2016}. We show that, although the mean field and
homogenization limits commute for finite times, they do not, in general,
commute in the long time limit. In particular, the bifurcation diagrams for the
stationary states can be different depending on the order with which we take
the two limits. Furthermore, we construct the bifurcation diagram for the
stationary McKean-Vlasov equation in a two-scale potential, before passing to
the homogenization limit, and we analyze the effect of the multiple local
minima in the confining potential on the number and the stability of stationary
solutions
Beliefs and actions in the trust game: creating instrumental variables to estimate the causal effect
In many economic contexts, an elusive variable of interest is the agent's expectation about relevant events, e.g. about other agents' behavior. Recent experimental studies as well as surveys have asked participants to state their beliefs explicitly, but little is known about the causal relation between beliefs and other behavioral variables. This paper discusses the possibility of creating exogenous instrumental variables for belief statements, by shifting the probabilities of the relevant events. We conduct trust game experiments where the amount sent back by
the second player (trustee) is exogenously varied by a random process, in a way that informs only the �first player (trustor) about the realized variation. The procedure
allows detecting causal links from beliefs to actions under plausible assumptions.
The IV estimates indicate a signi�ficant causal effect, comparable to the connection
between beliefs and actions that is suggested by OLS analyses
Supersymmetric Extension of the Quantum Spherical Model
In this work, we present a supersymmetric extension of the quantum spherical
model, both in components and also in the superspace formalisms. We find the
solution for short/long range interactions through the imaginary time formalism
path integral approach. The existence of critical points (classical and
quantum) is analyzed and the corresponding critical dimensions are determined.Comment: 21 pages, fixed notation to match published versio
Energy and volume of vector fields on spherical domains
We present in this paper a \boundary version" for theorems about minimality
of volume and energy functionals on a spherical domain of threedimensional
Euclidean sphere
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
A higher grading affine algebraic construction of integrable hierarchies,
containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is
proposed. We show that a two-component generalization of the Sch\" afer-Wayne
short pulse equation arises quite naturally from the first negative flow of the
WKI hierarchy. Some novel integrable nonautonomous models are also proposed.
The conserved charges, both local and nonlocal, are obtained from the Riccati
form of the spectral problem. The loop-soliton solutions of the WKI hierarchy
are systematically constructed through gauge followed by reciprocal B\" acklund
transformation, establishing the precise connection between the whole WKI and
AKNS hierarchies. The connection between the short pulse equation with the
sine-Gordon model is extended to a correspondence between the two-component
short pulse equation and the Lund-Regge model
The algebraic structure behind the derivative nonlinear Schroedinger equation
The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\"
odinger equation (DNLSE) amongst others interesting and important nonlinear
integrable equations. In this paper, a general higher grading affine algebraic
construction of integrable hierarchies is proposed and the KN hierarchy is
established in terms of a Kac-Moody algebra and principal
gradation. In this form, our spectral problem is linear in the spectral
parameter. The positive and negative flows are derived, showing that some
interesting physical models arise from the same algebraic structure. For
instance, the DNLSE is obtained as the second positive, while the Mikhailov
model as the first negative flows, respectively. The equivalence between the
latter and the massive Thirring model is explicitly demonstrated also. The
algebraic dressing method is employed to construct soliton solutions in a
systematic manner for all members of the hierarchy. Finally, the equivalence of
the spectral problem introduced in this paper with the usual one, which is
quadratic in the spectral parameter, is achieved by setting a particular
automorphism of the affine algebra, which maps the homogeneous into principal
gradation.Comment: references adde
Disagreement between capture probabilities extracted from capture and quasi-elastic backscattering excitation functions
Experimental quasi-elastic backscattering and capture (fusion) excitation
functions are usually used to extract the s-wave capture probabilities for the
heavy-ion reactions. We investigated the
O+Sn,Sm,Pb systems at energies near and below
the corresponding Coulomb barriers and concluded that the probabilities
extracted from quasi-elastic data are much larger than the ones extracted from
fusion excitation functions at sub and deep-sub barrier energies. This seems to
be a reasonable explanation for the known disagreement observed in literature
for the nuclear potential diffuseness derived from both methods.Comment: 9 pages, 3 figure
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