5,008 research outputs found
Regularizing effect and local existence for non-cutoff Boltzmann equation
The Boltzmann equation without Grad's angular cutoff assumption is believed
to have regularizing effect on the solution because of the non-integrable
angular singularity of the cross-section. However, even though so far this has
been justified satisfactorily for the spatially homogeneous Boltzmann equation,
it is still basically unsolved for the spatially inhomogeneous Boltzmann
equation. In this paper, by sharpening the coercivity and upper bound estimates
for the collision operator, establishing the hypo-ellipticity of the Boltzmann
operator based on a generalized version of the uncertainty principle, and
analyzing the commutators between the collision operator and some weighted
pseudo differential operators, we prove the regularizing effect in all (time,
space and velocity) variables on solutions when some mild regularity is imposed
on these solutions. For completeness, we also show that when the initial data
has this mild regularity and Maxwellian type decay in velocity variable, there
exists a unique local solution with the same regularity, so that this solution
enjoys the regularity for positive time
Cyclotron radiation and emission in graphene
Peculiarity in the cyclotron radiation and emission in graphene is
theoretically examined in terms of the optical conductivity and relaxation
rates to propose that graphene in magnetic fields can be a candidate to realize
the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf
48}, 559 (1986)].Comment: 4 pages, 3 figure
Effect of the atmosphere on the classification of LANDSAT data
The author has identified the following significant results. In conjunction with Turner's model for the correction of satellite data for atmospheric interference, the LOWTRAN-3 computer was used to calculate the atmospheric interference. Use of the program improved the contrast between different natural targets in the MSS LANDSAT data of Brasilia, Brazil. The classification accuracy of sugar canes was improved by about 9% in the multispectral data of Ribeirao Preto, Sao Paulo
Global existence and full regularity of the Boltzmann equation without angular cutoff
We prove the global existence and uniqueness of classical solutions around an
equilibrium to the Boltzmann equation without angular cutoff in some Sobolev
spaces. In addition, the solutions thus obtained are shown to be non-negative
and in all variables for any positive time. In this paper, we study
the Maxwellian molecule type collision operator with mild singularity. One of
the key observations is the introduction of a new important norm related to the
singular behavior of the cross section in the collision operator. This norm
captures the essential properties of the singularity and yields precisely the
dissipation of the linearized collision operator through the celebrated
H-theorem
Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory
This paper is devoted to studying symmetries of k-symplectic Hamiltonian and
Lagrangian first-order classical field theories. In particular, we define
symmetries and Cartan symmetries and study the problem of associating
conservation laws to these symmetries, stating and proving Noether's theorem in
different situations for the Hamiltonian and Lagrangian cases. We also
characterize equivalent Lagrangians, which lead to an introduction of
Lagrangian gauge symmetries, as well as analyzing their relation with Cartan
symmetries.Comment: 29 page
Understanding the Social Science Effect: An Intervention in Life Course Generosity
Does interacting with social science data in early adulthood promote generosity? To investigate this question from a life course development perspective, two distinct samples were drawn for a survey with an embedded experimental design. The first sample is of emerging adult college students (n = 30, median age = 20 years). The second sample is of young adults who were selected to participate based on their prior participation in a nationally representative and longitudinal study (n = 170, median age = 31 years). Toward the end of the survey, participants were randomly selected into a website interaction with either: (a) data on charitable giving, (b) data on social inequality, or (c) data about weather (a control condition). The key outcome of interest is a behavioral measure of generosity: whether participants elected to keep their study incentive or donate their incentive to a charitable organization. The donation decision occurred after the randomly selected website interaction. Interacting with charitable giving data resulted in greater generosity than interacting with weather data, across both samples. Interacting with social inequality data had mixed results. Moreover, emerging adult college students gave at a considerably higher rate overall than the national sample of young adults, net of treatment type. Implications are discussed
Influence of Magnetic Moment Formation on the Conductance of Coupled Quantum Wires
In this report, we develop a model for the resonant interaction between a
pair of coupled quantum wires, under conditions where self-consistent effects
lead to the formation of a local magnetic moment in one of the wires. Our
analysis is motivated by the experimental results of Morimoto et al. [Appl.
Phys. Lett. \bf{82}, 3952 (2003)], who showed that the conductance of one of
the quantum wires exhibits a resonant peak at low temperatures, whenever the
other wire is swept into the regime where local-moment formation is expected.
In order to account for these observations, we develop a theoretical model for
the inter-wire interaction that calculated the transmission properties of one
(the fixed) wire when the device potential is modified by the presence of an
extra scattering term, arising from the presence of the local moment in the
swept wire. To determine the transmission coefficients in this system, we
derive equations describing the dynamics of electrons in the swept and fixed
wires of the coupled-wire geometry. Our analysis clearly shows that the
observation of a resonant peak in the conductance of the fixed wire is
correlated to the appearance of additional structure (near or
) in the conductance of the swept wire, in agreement with the
experimental results of Morimoto et al
Probing the microscopic structure of bound states in quantum point contacts
Using an approach that allows us to probe the electronic structure of
strongly pinched-off quantum point contacts (QPCs), we provide evidence for the
formation of self-consistently realized bound states (BSs) in these structures.
Our approach exploits the resonant interaction between closely-coupled QPCs,
and demonstrates that the BSs may give rise to a robust confinement of single
spins, which show clear Zeeman splitting in a magnetic field
- …