Página 1 dos resultados de 435 itens digitais encontrados em 0.021 segundos

## Thermodynamic Perturbation Theory for Associating Fluids: Beyond First Order

Fonte: Universidade Rice
Publicador: Universidade Rice

ENG

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45.88%

#Statistical mechanics#Thermodynamics#Hydrogen bond#Equation of state#Patchy colloid#Association#Chemical engineering

Association interactions such as the hydrogen bond are a key component in many physical and biological systems. For this reason accurate theories are needed to describe both the thermodynamics and self – assembly of associating species. Applications of these theories range from those of industrial importance, such as equations of state for process simulations, to the realm of materials science where these theories can be used to predict how molecular structure determines the self – assembly of associating species into advanced supramolecular materials. Semi – empirical equations of state based on chemical or lattice theories do not contain the molecular level detail to make predictions on how molecular structure affects self – assembly of associating species. For this, one needs a theory whose starting point is the interaction potential between two associating species which includes this molecular level detail.
Development of accurate molecular theories for associating fluids is hampered by the strength, directionality and limited valence of the association interaction. This has proven particularly true in the extension of Mayer’s cluster theory to these associating fluids. This problem was largely solved by Wertheim in the 1980’s who developed an exact cluster expansion using a multi – density formalism. Wertheim’s cluster theory incorporates the geometry of the association interaction at an early point in the derivation. This allowed Wertheim to develop the theory in such a way that accurate and simple approximation methods could be applied such as thermodynamic perturbation theory (TPT). When treated at first order in perturbation (TPT1)...

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## Relative perturbation theory for diagonally dominant matrices

Fonte: Society for Industrial and Applied Mathematics
Publicador: Society for Industrial and Applied Mathematics

Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article

Publicado em /10/2014
ENG

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86.08%

#Accurate computations#Diagonally dominant matrices#Diagonally dominant parts#Eigenvalues#Inverses#Linear systems#Relative perturbation theory#Singular values#Eigenvalues and eigenfunctions#Inverse problems#Matrix algebra

In this paper, strong relative perturbation bounds are developed for a number of linear algebra problems involving diagonally dominant matrices. The key point is to parameterize diagonally dominant matrices using their off-diagonal entries and diagonally dominant parts and to consider small relative componentwise perturbations of these parameters. This allows us to obtain new relative perturbation bounds for the inverse, the solution to linear systems, the symmetric indefinite eigenvalue problem, the singular value problem, and the nonsymmetric eigenvalue problem. These bounds are much stronger than traditional perturbation results, since they are independent of either the standard condition number or the magnitude of eigenvalues/singular values. Together with previously derived perturbation bounds for the LDU factorization and the symmetric positive definite eigenvalue problem, this paper presents a complete and detailed account of relative structured perturbation theory for diagonally dominant matrices.; This research was partially supported by the Ministerio de Economía y Competitividad of Spain under grant MTM2012-32542.

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## A new perturbation bound for the LDU factorization of diagonally dominant matrices

Fonte: Society for Industrial and Applied Mathematics
Publicador: Society for Industrial and Applied Mathematics

Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article

Publicado em /07/2014
ENG

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55.9%

#Accurate computations#column diagonal dominance pivoting#diagonally dominant matrices#LDU factorization#rank-revealing decomposition#relative perturbation theory#diagonally dominant parts#Matemáticas

This work introduces a new perturbation bound for the L factor of the LDU factorization
of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting
strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU
factorization is guaranteed to be a rank-revealing decomposition. The new bound together with
those for the D and U factors in [F. M. Dopico and P. Koev, Numer. Math., 119 (2011), pp. 337–
371] establish that if diagonally dominant matrices are parameterized via their diagonally dominant
parts and off-diagonal entries, then tiny relative componentwise perturbations of these parameters
produce tiny relative normwise variations of L and U and tiny relative entrywise variations of D when
column diagonal dominance pivoting is used. These results will allow us to prove in a follow-up work
that such perturbations also lead to strong perturbation bounds for many other problems involving
diagonally dominant matrices.; Research supported in part by Ministerio de Economía y Competitividad
of Spain under grant MTM2012-32542.

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## Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/07/2009

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55.77%

#Mathematical Physics#Condensed Matter - Statistical Mechanics#High Energy Physics - Theory#Quantum Physics

A simple approximate solution for the quantum-mechanical quartic oscillator
$V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is
presented. It is based on a combining of perturbation theory near true minima
of the potential, semi-classical approximation at large distances and a
description of tunneling under the barrier. It provides 9-10 significant digits
in energies and gives for wavefunctions the relative deviation in real
$x$-space less than $\lesssim 10^{-3}$.; Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at
strong coupling (Shifmania)", Minneapolis, May 14-17, 2009

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## A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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45.95%

#Astrophysics - Cosmology and Nongalactic Astrophysics#Astrophysics - Instrumentation and Methods for Astrophysics

Subject of this paper is a detailed analysis of the PINOCCHIO algorithm for
studying the relative velocity statistics of merging haloes in Lagrangian
perturbation theory. Given a cosmological background model, a power spectrum of
fluctuations as well as a Gaussian linear density contrast field $\delta_{\rm
l}$ is generated on a cubic grid, which is then smoothed repeatedly with
Gaussian filters. For each Lagrangian particle at position $\bmath{q}$ and each
smoothing radius $R$, the collapse time, the velocities and ellipsoidal
truncation are computed using Lagrangian Perturbation Theory. The collapsed
medium is then fragmented into isolated objects by an algorithm designed to
mimic the accretion and merger events of hierarchical collapse. Directly after
the fragmentation process the mass function, merger histories of haloes and the
statistics of the relative velocities at merging are evaluated. We
reimplemented the algorithm in C++, recovered the mass function and optimised
the construction of halo merging histories. Comparing our results with the
output of the Millennium simulation suggests that PINOCCHIO is well suited for
studying relative velocities of merging haloes and is able to reproduce the
pairwise velocity distribution.; Comment: 10 pages...

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## Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.79%

We compute the lattice spacing corrections to the spectral density of the
Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO.
We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey
the relative power counting $m\sim a \Lambda_{\rm QCD}^2$: in this situation
discretisation effects can be treated as perturbation of the continuum
behaviour. While this framework fails to describe lattice spectral density
close to the threshold, it allows nevertheless to investigate important
properties of the spectrum of the Wilson Dirac operator. We discuss the range
of validity of our results and the possible implications in understanding the
phase diagram of Wilson fermions.; Comment: 27 pages, 4 figures; few typos corrected, added footnote, published
version

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## High-Order Corrections to the Lipatov Asymptotics in the \phi^4 Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/09/2005

Relevância na Pesquisa

45.8%

#High Energy Physics - Phenomenology#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#High Energy Physics - Theory

High orders in perturbation theory can be calculated by the Lipatov method.
For most field theories, the Lipatov asymptotics has the functional form c a^N
\Gamma(N+b) (N is the order of perturbation theory); relative corrections to
this asymptotics have the form of a power series in 1/N. The coefficients of
high order terms of this series can be calculated using a procedure analogous
to the Lipatov approach and are determined by the second instanton in the
considered field theory. These coefficients are calculated quantitatively for
the n-component \phi^4 theory under the assumption that the second instanton is
(i) a combination of two elementary instantons and (ii) a spherically
asymmetric localized function. The technique of two-instanton calculations is
developed, as well as the method for integrating over rotations of an
asymmetric instanton in the coordinate state.; Comment: 20 pages, PDF

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## 2-Nucleon 1-Loop Corrections to Pion Double Charge Exchange within Heavy Baryon Chiral Perturbation Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

55.77%

One-loop corrections at the two-nucleon level to Pion Double Charge exchange
(DCX) scattering off a nuclear target at threshold, are calculated within the
framework of Heavy Baryon Chiral Perturbation Theory (HBChPT). An estimate for
the (2-nucleon) 1-loop correction is obtained in the static limit and using an
impulse approximation. We find a small (1.6%) increase relative to the leading
order tree graphs.; Comment: 30 pages, RevTex, 5 tables, 5 ps figures; estimate of single-nucleon
1-loop corrections to the pi-pi, pi-N, 3pi-N vertices included in Section VI;
references added; clarifying remarks regarding notations and new results
related to 1-loop integrals included; discussion on Weinberg's power counting
rule expanded; this revised version to appear in PRC

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## Structure of the two-neutrino double-$\beta$ decay matrix elements within perturbation theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/06/2015

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The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are
studied within an exactly solvable model, which allows a violation of both
spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with
generators of the SO(8) group. It is found that this model reproduces the main
features of realistic calculation within the quasiparticle random-phase
approximation with isospin symmetry restoration concerning the dependence of
the two-neutrino double-$\beta$ decay matrix elements on isovector and
isoscalar particle-particle interactions. By using perturbation theory an
explicit dependence of the two-neutrino double-$\beta$ decay matrix elements on
the like-nucleon pairing, particle-particle T=0 and T=1, and particle-hole
proton-neutron interactions is obtained. It is found that double-$\beta$ decay
matrix elements do not depend on the mean field part of Hamiltonian and that
they are governed by a weak violation of both SU(2) and SU(4) symmetries by the
particle-particle interaction of Hamiltonian. It is pointed out that there is a
dominance of two-neutrino double-$\beta$ decay transition through a single
state of intermediate nucleus. The energy position of this state relative to
energies of initial and final ground states is given by a combination of
strengths of residual interactions. Further...

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## Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/08/2012

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45.79%

The infrared divergences of massless n-parton scattering amplitudes can be
derived from the anomalous dimension of n-jet operators in soft-collinear
effective theory. Up to three-loop order, the latter has been shown to have a
very simple structure: it contains pairwise color-dipole interactions among the
external partons, governed by the cusp anomalous dimension and a logarithm of
the kinematic invariants s_{ij}, plus a possible three-loop correlation
involving four particles, which is described by a yet unknown function of
conformal cross ratios of kinematic invariants. This function is constrained by
two-particle collinear limits and by the known behavior of amplitudes in the
high-energy limit. We construct a class of relatively simple functions
satisfying these constraints. We also extend the analysis to four-loop order,
finding that three additional four-particle correlations and a single
five-particle correlation appear, which again are governed by functions of
conformal cross ratios. Our results suggest that the dipole conjecture, which
states that only two-particle color-dipole correlations appear in the anomalous
dimension, may need to be generalized. We present a weaker form of the
conjecture, stating that to all orders in perturbation theory corrections to
the dipole formula are governed by functions of conformal cross ratios...

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## The Effective Field Theory of Dark Matter and Structure Formation: Semi-Analytical Results

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.81%

#Astrophysics - Cosmology and Nongalactic Astrophysics#General Relativity and Quantum Cosmology#High Energy Physics - Phenomenology#High Energy Physics - Theory

Complimenting recent work on the effective field theory of cosmological large
scale structures, here we present detailed approximate analytical results and
further pedagogical understanding of the method. We start from the
collisionless Boltzmann equation and integrate out short modes of a dark
matter/dark energy dominated universe (LambdaCDM) whose matter is comprised of
massive particles as used in cosmological simulations. This establishes a long
distance effective fluid, valid for length scales larger than the non-linear
scale ~ 10 Mpc, and provides the complete description of large scale structure
formation. Extracting the time dependence, we derive recursion relations that
encode the perturbative solution. This is exact for the matter dominated era
and quite accurate in LambdaCDM also. The effective fluid is characterized by
physical parameters, including sound speed and viscosity. These two fluid
parameters play a degenerate role with each other and lead to a relative
correction from standard perturbation theory of the form ~ 10^{-6}c^2k^2/H^2.
Starting from the linear theory, we calculate corrections to cosmological
observables, such as the baryon-acoustic-oscillation peak, which we compute
semi-analytically at one-loop order. Due to the non-zero fluid parameters...

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## Utility of Galilean Symmetry in Light-Front Perturbation Theory: A Nontrivial Example in QCD

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/02/1998

Relevância na Pesquisa

45.78%

Investigations have revealed a very complex structure for the coefficient
functions accompanying the divergences for individual time ($x^+$) ordered
diagrams in light-front perturbation theory. No guidelines seem to be available
to look for possible mistakes in the structure of these coefficient functions
emerging at the end of a long and tedious calculation, in contrast to covariant
field theory. Since, in light-front field theory, transverse boost generator is
a kinematical operator which acts just as the two-dimensional Galilean boost
generator in non-relativistic dynamics, it may provide some constraint on the
resulting structures. In this work we investigate the utility of Galilean
symmetry beyond tree level in the context of coupling constant renormalization
in light-front QCD using the two-component formalism. We show that for each
$x^+$ ordered diagram separately, underlying transverse boost symmetry fixes
relative signs of terms in the coefficient functions accompanying the diverging
logarithms. We also summarize the results leading to coupling constant
renormalization for the most general kinematics.; Comment: RevTeX, five PostScript figures

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## Loop Corrections in Non-Linear Cosmological Perturbation Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/09/1995

Relevância na Pesquisa

45.87%

Using a diagrammatic approach to Eulerian perturbation theory, we
analytically calculate the variance and skewness of the density and velocity
divergence induced by gravitational evolution from Gaussian initial conditions,
including corrections *beyond* leading order. Except for the power spectrum,
previous calculations in cosmological perturbation theory have been confined to
leading order (tree level)-we extend these to include loop corrections. For
scale-free initial power spectra, the one-loop variance \sigma^2 = \sigma^2_l +
1.82 \sigma^4_l and the skewness S_3 = 34/7 + 9.8 \sigma^2_l, where \sigma_l is
the rms fluctuation of the linear density field. We also compute loop
corrections to the variance, skewness, and kurtosis for several non-linear
approximation schemes, where the calculation can be easily generalized to
1-point cumulants of higher order and arbitrary number of loops. We find that
the Zel'dovich approximation gives the best approximation to the loop
corrections of exact perturbation theory, followed by the Linear Potential
approximation (LPA) and the Frozen Flow approximation (FFA), in qualitative
agreement with the relative behavior of tree-level results. In LPA and FFA,
loop corrections are infrared divergent for spectral indices n < 0; this is
related to the breaking of Galilean invariance in these schemes.; Comment: 53 pages...

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## Cosmological perturbation theory for baryons and dark matter I: one-loop corrections in the RPT framework

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

55.77%

We generalize the `renormalized' perturbation theory (RPT) formalism of
Crocce & Scoccimarro (2006a) to deal with multiple fluids in the Universe and
here we present calculations up to the one-loop level. We apply the approach to
the non-linear evolution of baryon and cold dark matter (CDM) perturbations,
evolving from distinct sets of initial conditions. In current models of
structure formation, it is standard practice to treat baryons and CDM as an
effective single component fluid. In this approximation, one uses a weighed sum
of late-time baryon and CDM transfer functions to set initial conditions. Here,
we explore whether this approach can be used for high precision work. We show
that, even for a pure linear treatment, there is a large-scale scale-dependent
bias between baryons and CDM for WMAP5 cosmology. This bias is >1% until the
present day, when it is driven towards unity through gravitational relaxation.
Using the RPT formalism we test this approximation in the non-linear regime,
and show that the CDM power spectrum in the 2-component fluid differs from that
obtained from a 1-component fluid by ~3% on scales of order k~0.05 h/Mpc at
z=10, and by ~0.5% at z=0. However, for the case of baryons the situation is
worse and we find that the power spectrum is suppressed by ~15% on scales
k~0.05 h/Mpc at z=10...

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## Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/04/1998

Relevância na Pesquisa

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We compute bulk properties of Heisenberg spin-1/2 ladders using
Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We
formulate a method to extract high-order perturbative coefficients in the bulk
limit from solutions for relatively small finite clusters. For example, a
perturbative calculation for an isotropic $2\times 12$ ladder yields an
eleventh-order estimate of the ground-state energy per site that is within
0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the
method also enables a reliable estimate of the radius of convergence of the
perturbative expansion. We find that for the rung basis the radius of
convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between
the coupling along the chain relative to the coupling across the chain. In
contrast, for the plaquette basis we estimate a radius of convergence of
$\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the
only currently available perturbative approach which can provide a reliable
treatment of the physically interesting case of isotropic $(\lambda=1)$ spin
ladders. We illustrate our methods by computing perturbative coefficients for
the ground-state energy per site, the gap, and the one-magnon dispersion
relation.; Comment: 22 pages. 9 figures

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## Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.79%

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field
theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary
matrix $R$ which represents the single gluon scattering matrix. We discuss the
peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We
develop a perturbative expansion in the RFT framework, and find several
eigenstates of the zeroth order Hamiltonian. The zeroth order of this
perturbation preserves the number of $s$ - channel gluons. The eigenstates have
a natural interpretation in terms of the $t$ - channel exchanges. Studying the
single $s$ - channel gluon sector we find the eigenstates which include the
reggeized gluon and five other colored Reggeons. In the two ($s$ - channel)
gluon sector we study only singlet color exchanges. We find five charge
conjugation even states. The bound state of two reggeized gluons is the
standard BFKL Pomeron. The intercepts of the other Pomerons in the large $N$
limit are $1+\omega_P=1+2\omega$ where $1+\omega$ is the intercept of the BFKL
Pomeron, but their coupling in perturbation theory is suppressed by at least
$1/N^2$ relative to the double BFKL Pomeron exchange. For the $[27,27]$ Pomeron
we find $\omega_{[27,27]}=2\omega+O(1/N)>2\omega$. We also find three charge
conjugation odd exchanges...

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## Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.84%

An acoustic oscillation of the primeval photon-baryon fluid around the
decoupling time imprints a characteristic scale in the galaxy distribution
today, known as the baryon acoustic oscillation (BAO) scale. Several on-going
and/or future galaxy surveys aim at detecting and precisely determining the BAO
scale so as to trace the expansion history of the universe. We consider
nonlinear and redshift-space distortion effects on the shifts of the BAO scale
in $k$-space using perturbation theory. The resulting shifts are indeed
sensitive to different choices of the definition of the BAO scale, which needs
to be kept in mind in the data analysis. We present a toy model to explain the
physical behavior of the shifts. We find that the BAO scale defined as in
Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative
to the prediction in {\it linear theory} in real space. The shifts can be
predicted accurately for scales where the perturbation theory is reliable.; Comment: 21 pages, 9 figures, references and supplementary sections added,
accepted for publication in PASJ

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## Peculiar Velocity, Cosmic Perturbation Theory and the CMB Anisotropy

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.85%

This is a somewhat extended version of the original July 93 report. It is
proved that the cosmological density perturbation is associated with a peculiar
velocity field. This allows a simple formulation of cosmological perturbation
theory, which works entirely with quasi-Newtonian fluid flow equations. As an
illustration, the large scale cosmic microwave background anisotropy
(Sachs-Wolfe effect) is calculated without any reference to the metric
perturbation. In addition, assuming the usual adiabatic initial condition on
the density perturbation, we show that the dipole of the anisotropy measures
our peculiar velocity relative to the average peculiar velocity within the last
scattering surface of the microwave background, thus defining its frame of
reference.; Comment: 9 pages, REVTEX, LANCS 9321

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## The Continuum Version of \phi^4_{1+1}-theory in Light-Front Quantization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/09/1997

Relevância na Pesquisa

45.79%

A genuine continuum treatment of the massive \phi^4_{1+1}-theory in
light-cone quantization is proposed. Fields are treated as operator valued
distributions thereby leading to a mathematically well defined handling of
ultraviolet and light cone induced infrared divergences and of their
renormalization. Although non-perturbative the continuum light cone approach is
no more complex than usual perturbation theory in lowest order. Relative to
discretized light cone quantization, the critical coupling increases by 30% to
a value r = 1.5. Conventional perturbation theory at the corresponding order
yields r_1=1, whereas the RG improved fourth order result is r_4 = 1.8 +-0.05.; Comment: 19 pages, 6 eps figures included, in Latex 2.09, uses psfig

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## Trends in R-X bond dissociation energies (R = Me, Et, i -Pr, t -Bu; X = H, CH 3 , OCH 3 , OH, F): a surprising shortcoming of density functional theory

Fonte: American Chemical Society
Publicador: American Chemical Society

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

55.91%

#Keywords: Chemical bonds#Error analysis#Perturbation techniques#Probability density function#Thermal effects#Absolute heats#Bond dissociation energy (BDE)#Second-order perturbation theory#Stabilizing effects#Dissociation

The performance of a variety of high-level composite procedures, as well as lower-cost density functional theory (DFT)- and second-order perturbation theory (MP2)-based methods, for the prediction of absolute and relative R-X bond dissociation energies (BDEs) was examined for R = Me, Et, i-Pr and t-Bu, and X = H, CH3, OCH3, OH and F. The methods considered include the high-level G3(MP2)-RAD and G3-RAD procedures, a variety of pure and hybrid DFT methods (B-LYP, B3-LYP, B3-P86, KMLYP, B1B95, MPW1PW91, MPW1B95, BB1K, MPW1K, MPWB1K and BMK), standard restricted (open-shell) MP2 (RMP2), and two recently introduced variants of MP2, namely spin-component-scaled MP2 (SCS-MP2) and scaled-opposite-spin MP2 (SOS-MP2). The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the lower-level DFT- and MP2-based procedures. The best DFT methods (KMLYP and particularly BMK) provide very reasonable predictions for the absolute heats of formation and R-X BDEs for the systems studied. However, all of the DFT methods overestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu, leading in some cases to incorrect qualitative behavior. In contrast, the MP2-based methods generally show larger errors (than the best DFT methods) in the absolute heats of formation and BDEs...

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