1,856 research outputs found
Weighted Low-Regularity Solutions of the KP-I Initial Value Problem
In this paper we establish local well-posedness of the KP-I problem, with
initial data small in the intersection of the natural energy space with the
space of functions which are square integrable when multiplied by the weight y.
The result is proved by the contraction mapping principle. A similar (but
slightly weaker) result was the main Theorem in the paper " Low regularity
solutions for the Kadomstev-Petviashvili I equation " by Colliander, Kenig and
Staffilani (GAFA 13 (2003),737-794 and math.AP/0204244). Ionescu found a
counterexample (included in the present paper) to the main estimate used in the
GAFA paper, which renders incorrect the proof there. The present paper thus
provides a correct proof of a strengthened version of the main result in the
GAFA paper
Transductive Learning with String Kernels for Cross-Domain Text Classification
For many text classification tasks, there is a major problem posed by the
lack of labeled data in a target domain. Although classifiers for a target
domain can be trained on labeled text data from a related source domain, the
accuracy of such classifiers is usually lower in the cross-domain setting.
Recently, string kernels have obtained state-of-the-art results in various text
classification tasks such as native language identification or automatic essay
scoring. Moreover, classifiers based on string kernels have been found to be
robust to the distribution gap between different domains. In this paper, we
formally describe an algorithm composed of two simple yet effective
transductive learning approaches to further improve the results of string
kernels in cross-domain settings. By adapting string kernels to the test set
without using the ground-truth test labels, we report significantly better
accuracy rates in cross-domain English polarity classification.Comment: Accepted at ICONIP 2018. arXiv admin note: substantial text overlap
with arXiv:1808.0840
Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory
The phi4 scalar field theory in three dimensions, prototype for the study of
phase transitions, is investigated by means of the hierarchical reference
theory (HRT) in its smooth cutoff formulation. The critical behavior is
described by scaling laws and critical exponents which compare favorably with
the known values of the Ising universality class. The inverse susceptibility
vanishes identically inside the coexistence curve, providing a first principle
implementation of the Maxwell construction, and shows the expected
discontinuity across the phase boundary, at variance with the usual sharp
cutoff implementation of HRT. The correct description of first and second order
phase transitions within a microscopic, nonperturbative approach is thus
achieved in the smooth cutoff HRT.Comment: 8 pages, 4 figure
A para-differential renormalization technique for nonlinear dispersive equations
For \alpha \in (1,2) we prove that the initial-value problem \partial_t
u+D^\alpha\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t;
u(0)=\phi, is globally well-posed in the space of real-valued L^2-functions. We
use a frequency dependent renormalization method to control the strong low-high
frequency interactions.Comment: 42 pages, no figure
Atomistic Simulation of Energetic and Entropic Elasticity in Short-chain Polyethylenes
The thermodynamical aspects of polymeric liquids subjected to uniaxial elongational flow are examined using atomistically detailed nonequilibrium Monte Carlo simulations. In particular, attention is paid to the energetic effects, in addition to the entropic ones, which occur under conditions of extreme deformation. Atomistic nonequilibrium Monte Carlo simulations of linear polyethylene systems, ranging in molecular length from C24 to C78 and for temperatures from 300 to 450 K, demonstrate clear contributions of energetic effects to the elasticity of the system. These are manifested in a conformationally dependent heat capacity, which is significant under large deformations. Violations of the hypothesis of purely entropic elasticity are evident in these simulations, in that the free energy of the system is demonstrated to be composed of significant energetic effects under high degrees of orientation. These arise mainly from favorable intermolecular side-to-side interactions developing in the process of elongation due to chain uncoiling and alignment in the direction of extension
Energetic and Entropic Elasticity of Nonisothermal Flowing Polymers: Experiment, Theory, and Simulation
The thermodynamical aspects of polymeric liquids subjected to nonisothermal flow are examined from the complementary perspectives of theory, experiment, and simulation. In particular, attention is paid to the energetic effects, in addition to the entropic ones, that occur under conditions of extreme deformation. Comparisons of experimental measurements of the temperature rise generated under elongational flow at high strain rates with macroscopic finite element simulations offer clear evidence of the persistence and importance of energetic effects under severe deformation. The performance of various forms of the temperature equation are evaluated with regard to experiment, and it is concluded that the standard form of this evolution equation, arising from the concept of purely entropic elasticity, is inadequate for describing nonisothermal flow processes of polymeric liquids under high deformation. Complete temperature equations, in the sense that they possess a direct and explicit dependence on the energetics of the microstructure of the material, provide excellent agreement with experimental data
Energetic and Entropic Elasticity of Nonisothermal Flowing Polymers: Experiment, Theory, and Simulation
The thermodynamical aspects of polymeric liquids subjected to nonisothermal flow are examined from the complementary perspectives of theory, experiment, and simulation. In particular, attention is paid to the energetic effects, in addition to the entropic ones, that occur under conditions of extreme deformation. Comparisons of experimental measurements of the temperature rise generated under elongational flow at high strain rates with macroscopic finite element simulations offer clear evidence of the persistence and importance of energetic effects under severe deformation. The performance of various forms of the temperature equation are evaluated with regard to experiment, and it is concluded that the standard form of this evolution equation, arising from the concept of purely entropic elasticity, is inadequate for describing nonisothermal flow processes of polymeric liquids under high deformation. Complete temperature equations, in the sense that they possess a direct and explicit dependence on the energetics of the microstructure of the material, provide excellent agreement with experimental data
Significance of small voltage in impedance spectroscopy measurements on electrolytic cells
We investigate, theoretically, for what amplitude of the applied voltage to an electrolytic cell the concept of impedance is meaningful. The analysis is performed by means of a continuum model, by assuming the electrodes perfectly blocking. We show that, in the low-frequency range, the electrolytic cell behaves as a linear system only if the amplitude of the measurement voltage is small with respect to the thermal voltage V(T)=k(B)T/q, where k(B)T is the thermal energy, and q is the modulus of the electrical charge of the ions, assumed identical except for the sign of the charge. On the contrary, for large frequency, we prove that the amplitude of the applied signal has to be small with respect to a critical voltage that is frequency dependent. The same kind of analysis is presented for the case in which the diffusion coefficients of the positive ions is different from that for negative ions, and for the case where surface adsorption takes place
Asymptotic channels and gauge transformations of the time-dependent Dirac equation for extremely relativistic heavy-ion collisions
We discuss the two-center, time-dependent Dirac equation describing the
dynamics of an electron during a peripheral, relativistic heavy-ion collision
at extreme energies. We derive a factored form, which is exact in the
high-energy limit, for the asymptotic channel solutions of the Dirac equation,
and elucidate their close connection with gauge transformations which transform
the dynamics into a representation in which the interaction between the
electron and a distant ion is of short range. We describe the implications of
this relationship for solving the time-dependent Dirac equation for extremely
relativistic collisions.Comment: 12 pages, RevTeX, 2 figures, submitted to PR
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