12,513 research outputs found
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
As a continuation of our series works on the Boltzmann equation without
angular cutoff assumption, in this part, the global existence of solution to
the Cauchy problem in the whole space is proved in some suitable weighted
Sobolev spaces for hard potential when the solution is a small perturbation of
a global equilibrium
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
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
DNA-psoralen: single-molecule experiments and first principles calculations
The authors measure the persistence and contour lengths of DNA-psoralen
complexes, as a function of psoralen concentration, for intercalated and
crosslinked complexes. In both cases, the persistence length monotonically
increases until a certain critical concentration is reached, above which it
abruptly decreases and remains approximately constant. The contour length of
the complexes exhibits no such discontinuous behavior. By fitting the relative
increase of the contour length to the neighbor exclusion model, we obtain the
exclusion number and the intrinsic intercalating constant of the psoralen-DNA
interaction. Ab initio calculations are employed in order to provide an
atomistic picture of these experimental findings.Comment: 9 pages, 4 figures in re-print format 3 pages, 4 figures in the
published versio
Is space a part of being? Reassessing space through Japanese thought
This paper adopts a hermeneutical approach to Japanese thought, in the light of Heideggerian thought, in order to reassess the way we understand space. In a first stage, a few ideas concerning Japanese language and aesthetics will be briefly addressed for a better understanding of how space is embraced in Japanese thought and culture (experience precedes description). We will then turn to the two main concepts: fūdo (milieu) and basho (place), coined by two 20th century philosophers: Watsuji Tetsurō and Nishida Kitarō. The logic behind fūdo is that a true awareness of space is built not from thinking about it – since we are already objectifying it and, therefore, understanding ourselves detached from it –, but from being in it; experiencing it. The concept of basho represents a more logical argument and allows us to focus on the relation between the particular and the universal; or, as we will see, between being and space. What we can conclude from the articulation and interpretation of these two concepts is that space is certainly more than just a pure geometrical concept or a receptacle where human beings exist – it can also be thought of as a part of being.info:eu-repo/semantics/publishedVersio
The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions
This is a continuation of our series of works for the inhomogeneous Boltzmann
equation. We study qualitative properties of classical solutions, precisely,
the full regularization in all variables, uniqueness, non-negativity and
convergence rate to the equilibrium. Together with the results of Parts I and
II about the well posedness of the Cauchy problem around Maxwellian, we
conclude this series with a satisfactory mathematical theory for Boltzmann
equation without angular cutoff
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