2,774 research outputs found
Random walk on the range of random walk
We study the random walk X on the range of a simple random walk on ℤ d in dimensions d≥4. When d≥5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin
Maximal -regularity for stochastic evolution equations
We prove maximal -regularity for the stochastic evolution equation
\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t),
\qquad t\in [0,T],
U(0) & = u_0, {aligned}. under the assumption that is a sectorial
operator with a bounded -calculus of angle less than on
a space . The driving process is a cylindrical
Brownian motion in an abstract Hilbert space . For and
and initial conditions in the real interpolation space
\XAp we prove existence of unique strong solution with trajectories in
L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities
F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to
\g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their
second variables with small enough Lipschitz constants. Extensions to the case
where is an adapted operator-valued process are considered as well.
Various applications to stochastic partial differential equations are worked
out in detail. These include higher-order and time-dependent parabolic
equations and the Navier-Stokes equation on a smooth bounded domain
\OO\subseteq \R^d with . For the latter, the existence of a unique
strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi
Four-nucleon shell-model calculations in a Faddeev-like approach
We use equations for Faddeev amplitudes to solve the shell-model problem for
four nucleons in the model space that includes up to 14 hbar Omega
harmonic-oscillator excitations above the unperturbed ground state. Two- and
three-body effective interactions derived from the Reid93 and Argonne V8'
nucleon-nucleon potentials are used in the calculations. Binding energies,
excitations energies, point-nucleon radii and electromagnetic and strangeness
charge form factors for 4He are studied. The structure of the Faddeev-like
equations is discussed and a formula for matrix elements of the permutation
operators in a harmonic-oscillator basis is given. The dependence on
harmonic-oscillator excitations allowed in the model space and on the
harmonic-oscillator frequency is investigated. It is demonstrated that the use
of the three-body effective interactions improves the convergence of the
results.Comment: 22 pages, 13 figures, REVTe
The Price of WMAP Inflation in Supergravity
The three-year data from WMAP are in stunning agreement with the simplest
possible quadratic potential for chaotic inflation, as well as with new or
symmetry-breaking inflation. We investigate the possibilities for incorporating
these potentials within supergravity, particularly of the no-scale type that is
motivated by string theory. Models with inflation driven by the matter sector
may be constructed in no-scale supergravity, if the moduli are assumed to be
stabilised by some higher-scale dynamics and at the expense of some
fine-tuning. We discuss specific scenarios for stabilising the moduli via
either D- or F-terms in the effective potential, and survey possible
inflationary models in the presence of D-term stabilisation.Comment: 15 pages, 6 figures, plain Late
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Observations of the diurnal cycle of outgoing longwave radiation from the Geostationary Earth Radiation Budget instrument
The Geostationary Earth Radiation Budget instrument on Meteosat-8, located over Africa, provides unprecedented temporal sampling (~17 minutes) of the broadband emitted thermal and reflected solar radiances. We analyse the diurnal cycle of the outgoing longwave radiation (OLR) fluxes derived from the thermal radiances for July 2006. Principal component (PC) analysis separates the signals of the surface temperature response to solar heating and of the development of convective clouds. The first two PCs explain most of the OLR variations: PC1 (surface heating) explains 82.3% of the total variance and PC2 (cloud development) explains 12.8% of the variance. Convection is initiated preferentially over mountainous regions and the cloud then advects downstream in the ambient flow. Diurnal variations are much weaker over the oceans, but a coherent signal over the Gulf of Guinea suggests that the cloudiness is modulated by the diurnally varying contrast between the Gulf and the adjacent land mass
Solutions of the Faddeev-Yakubovsky equations for the four nucleons scattering states
The Faddeev-Yakubowsky equations in configuration space have been solved for
the four nucleon system. The results with an S-wave interaction model in the
isospin approximation are presented. They concern the bound and scattering
states below the first three-body threshold. The elastic phase-shifts for the
N+NNN reaction in different () channels are given and the corresponding
low energy expansions are discussed. Particular attention is payed to the n+t
elastic cross section. Its resonant structure is well described in terms of a
simple NN interaction. First results concerning the S-matrix for the coupled
N+NNN-NN+NN channels and the strong deuteron-deuteron scattering length are
obtained.Comment: latex.tar.gz, 36 pages, 10 figures, 11 tables. To be published in
Physical Review
The Ay Problem for p-3He Elastic Scattering
We present evidence that numerically accurate quantum calculations employing
modern internucleon forces do not reproduce the proton analyzing power, A_y,
for p-3He elastic scattering at low energies. These calculations underpredict
new measured analyzing powers by approximately 30% at E_{c.m.} = 1.20 MeV and
by 40% at E_{c.m.} = 1.69 MeV, an effect analogous to a well-known problem in
p-d and n-d scattering. The calculations are performed using the complex Kohn
variational principle and the (correlated) Hyperspherical Harmonics technique
with full treatment of the Coulomb force. The inclusion of the three-nucleon
interaction does not improve the agreement with the experimental data.Comment: Latex file, 4 pages, 2 figures, to be published on Phys. Rev. Let
Anomalous U(1) D-term Contribution in Type I String Models
We study the -term contribution for anomalous U(1) symmetries in type I
string models and derive general formula for the -term contribution,
assuming that the dominant source of SUSY breaking is given by -terms of the
dilaton, (overall) moduli or twisted moduli fields. On the basis of the
formula, we also point out that there are several different features from the
case in heterotic string models. The differences originate from the different
forms of K\"ahler potential between twisted moduli fields in type I string
models and the dilaton field in heterotic string models.Comment: 16 pages, latex, no figur
Reaction mechanism and characteristics of T_{20} in d + ^3He backward elastic scattering at intermediate energies
For backward elastic scattering of deuterons by ^3He, cross sections \sigma
and tensor analyzing power T_{20} are measured at E_d=140-270 MeV. The data are
analyzed by the PWIA and by the general formula which includes virtual
excitations of other channels, with the assumption of the proton transfer from
^3He to the deuteron. Using ^3He wave functions calculated by the Faddeev
equation, the PWIA describes global features of the experimental data, while
the virtual excitation effects are important for quantitative fits to the
T_{20} data. Theoretical predictions on T_{20}, K_y^y (polarization transfer
coefficient) and C_{yy} (spin correlation coefficient) are provided up to GeV
energies.Comment: REVTEX+epsfig, 17 pages including 6 eps figs, to be published in
Phys. Rev.
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