21,845 research outputs found
Multivariate Fitting and the Error Matrix in Global Analysis of Data
When a large body of data from diverse experiments is analyzed using a
theoretical model with many parameters, the standard error matrix method and
the general tools for evaluating errors may become inadequate. We present an
iterative method that significantly improves the reliability of the error
matrix calculation. To obtain even better estimates of the uncertainties on
predictions of physical observables, we also present a Lagrange multiplier
method that explores the entire parameter space and avoids the linear
approximations assumed in conventional error propagation calculations. These
methods are illustrated by an example from the global analysis of parton
distribution functions.Comment: 13 pages, 5 figures, Latex; minor clarifications, fortran program
made available; Normalization of Hessian matrix changed to HEP standar
Cantor type functions in non-integer bases
Cantor's ternary function is generalized to arbitrary base-change functions
in non-integer bases. Some of them share the curious properties of Cantor's
function, while others behave quite differently
Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions
We present a new algorithm for quantum Monte Carlo simulation based on global
updating with loops. While various theoretical predictions are confirmed in one
dimension, we find, for S=1 systems on a square lattice with an
antiferromagnetic biquadratic interaction, that the intermediate phase between
the antiferromagnetic and the ferromagnetic phases is disordered and that the
two phase transitions are both of the first order in contrast to the
one-dimensional case. It is strongly suggested that the transition points
coincide those at which the algorithm changes qualitatively.Comment: 4 pages including 4 figures, to appear in JPS
Relaxation of a Single Knotted Ring Polymer
The relaxation of a single knotted ring polymer is studied by Brownian
dynamics simulations. The relaxation rate lambda_q for the wave number q is
estimated by the least square fit of the equilibrium time-displaced correlation
function to a double exponential decay at long times. The relaxation rate
distribution of a single ring polymer with the trefoil knot appears to behave
as lambda_q=A(1/N^)x for q=1 and lambda_q=A'(q/N)^x' for q=2 and 3, where
x=2.61, x'=2.02 and A>A'. The wave number q of the slowest relaxation rate for
each N is given by q=2 for small values of N, while it is given by q=1 for
large values of N. This crossover corresponds to the change of the structure of
the ring polymer caused by the localization of the knotted part to a part of
the ring polymer.Comment: 13 pages, 5 figures, uses jpsj2.cl
Phase diagram of aggregation of oppositely charged colloids in salty water
Aggregation of two oppositely charged colloids in salty water is studied. We
focus on the role of Coulomb interaction in strongly asymmetric systems in
which the charge and size of one colloid is much larger than the other one. In
the solution, each large colloid (macroion) attracts certain number of
oppositely charged small colloids (-ion) to form a complex. If the
concentration ratio of the two colloids is such that complexes are not strongly
charged, they condense in a macroscopic aggregate. As a result, the phase
diagram in a plane of concentrations of two colloids consists of an aggregation
domain sandwiched between two domains of stable solutions of complexes. The
aggregation domain has a central part of total aggregation and two wings
corresponding to partial aggregation. A quantitative theory of the phase
diagram in the presence of monovalent salt is developed. It is shown that as
the Debye-H\"{u}ckel screening radius decreases, the aggregation domain
grows, but the relative size of the partial aggregation domains becomes much
smaller. As an important application of the theory, we consider solutions of
long double-helix DNA with strongly charged positive spheres (artificial
chromatin). We also consider implications of our theory for in vitro
experiments with the natural chromatin. Finally, the effect of different shapes
of macroions on the phase diagram is discussed.Comment: 10 pages, 9 figures. The text is rewritten, but results are not
change
Valley splitting of Si/SiGe heterostructures in tilted magnetic fields
We have investigated the valley splitting of two-dimensional electrons in
high quality Si/SiGe heterostructures under tilted magnetic fields.
For all the samples in our study, the valley splitting at filling factor
() is significantly different before and after the
coincidence angle, at which energy levels cross at the Fermi level. On both
sides of the coincidence, a linear density dependence of on the
electron density was observed, while the slope of these two configurations
differs by more than a factor of two. We argue that screening of the Coulomb
interaction from the low-lying filled levels, which also explains the observed
spin-dependent resistivity, is responsible for the large difference of
before and after the coincidence.Comment: REVTEX 4 pages, 4 figure
Nonlinearities in Conservative Growth Equations
Using the dynamic renormalization group (DRG) technique, we analyze general
nonlinearities in a conservative nonlinear growth equation with non-conserved
gaussian white noise. We show that they fall in two classes only: the
Edwards-Wilkinson and Lai-Das Sarma types, by explicitly computing the
associated amputated two and three point functions at the first order in
perturbation parameter(s). We further generalize this analysis to higher order
nonlinearities and also suggest a physically meaningful geometric
interpretation of the same.Comment: REVTEX, will appear in Phys Rev E Rapid Comm. February 1996, .ps
figure file available upon request to [email protected]
Precision measurement of the fundamental vibrational frequencies of tritium-bearing hydrogen molecules: T, DT, HT
High-resolution coherent Raman spectroscopic measurements of all three
tritium-containing molecular hydrogen isotopologues T, DT and HT were
performed to determine the ground electronic state fundamental Q-branch () transition frequencies at accuracies of
cm. An over hundred-fold improvement in accuracy over previous
experiments allows the comparison with the latest ab initio calculations in the
framework of Non-Adiabatic Perturbation Theory including nonrelativisitic,
relativisitic and QED contributions. Excellent agreement is found between
experiment and theory, thus providing a verification of the validity of the
NAPT-framework for these tritiated species. While the transition frequencies
were corrected for ac-Stark shifts, the contributions of non-resonant
background as well as quantum interference effects between resonant features in
the nonlinear spectroscopy were quantitatively investigated, also leading to
corrections to the transition frequencies. Methods of saturated CARS with the
observation of Lamb dips, as well as the use of continuous-wave radiation for
the Stokes frequency were explored, that might pave the way for future
higher-accuracy CARS measurements.Comment: 15 pages, 13 figure
Casimir Force on Real Materials - the Slab and Cavity Geometry
We analyse the potential of the geometry of a slab in a planar cavity for the
purpose of Casimir force experiments. The force and its dependence on
temperature, material properties and finite slab thickness are investigated
both analytically and numerically for slab and walls made of aluminium and
teflon FEP respectively. We conclude that such a setup is ideal for
measurements of the temperature dependence of the Casimir force. By numerical
calculation it is shown that temperature effects are dramatically larger for
dielectrics, suggesting that a dielectric such as teflon FEP whose properties
vary little within a moderate temperature range, should be considered for
experimental purposes. We finally discuss the subtle but fundamental matter of
the various Green's two-point function approaches present in the literature and
show how they are different formulations describing the same phenomenon.Comment: 24 pages, 11 figures; expanded discussion, one appendix added, 1 new
figure and 10 new references. To appear in J. Phys. A: Math. Theo
Rigorous definition of oxidation states of ions in solids
We present justification and rigorous procedure for electron partitioning
among atoms in extended systems. The method is based on wavefunction topology
and the modern theory of polarization, rather than charge density partitioning
or wavefunction projection, and, as such, re-formulates the concept of
oxidation state without assuming real-space charge transfer between atoms. This
formulation provides rigorous electrostatics of finite extent solids, including
films and nanowires.Comment: 4 pages, 3 figure
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