94 research outputs found
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
Tension and stiffness of the hard sphere crystal-fluid interface
A combination of fundamental measure density functional theory and Monte
Carlo computer simulation is used to determine the orientation-resolved
interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid
interface. Microscopic density functional theory is in quantitative agreement
with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small
anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the
(001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is
denoting the thermal energy and \sigma the hard sphere diameter. We compare our
results with existing experimental findings
Generalized r-matrix structure and algebro-geometric solution for integrable systems
The purpose of this paper is to construct a generalized r-matrix structure of
finite dimensional systems and an approach to obtain the algebro-geometric
solutions of integrable nonlinear evolution equations (NLEEs). Our starting
point is a generalized Lax matrix instead of usual Lax pair. The generalized
r-matrix structure and Hamiltonian functions are presented on the basis of
fundamental Poisson bracket. It can be clearly seen that various nonlinear
constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV,
c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure.
All these nonlinear systems have {\it r}-matrices, and are completely
integrable in Liouville's sense. Furthermore, our generalized structure is
developed to become an approach to obtain the algebro-geometric solutions of
integrable NLEEs. Finally, the two typical examples are considered to
illustrate this approach: the infinite or periodic Toda lattice equation and
the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure
Classical Poisson structures and r-matrices from constrained flows
We construct the classical Poisson structure and -matrix for some finite
dimensional integrable Hamiltonian systems obtained by constraining the flows
of soliton equations in a certain way. This approach allows one to produce new
kinds of classical, dynamical Yang-Baxter structures. To illustrate the method
we present the -matrices associated with the constrained flows of the
Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a
2-dimensional eigenvalue problem. Some of the obtained -matrices depend only
on the spectral parameters, but others depend also on the dynamical variables.
For consistency they have to obey a classical Yang-Baxter-type equation,
possibly with dynamical extra terms.Comment: 16 pages in LaTe
Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy
Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different
from the original ones. Binary nonlinearization procedure corresponding to the
Bargmann symmetry constraint is carried out for those Lax pairs. The proposed
Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of
commutative, finite dimensional integrable Hamiltonian systems in the Liouville
sense, which also provides us with new examples of finite dimensional
integrable Hamiltonian systems. A sort of involutive solutions to the
Kaup-Newell hierarchy are exhibited through the obtained finite dimensional
integrable systems and the general involutive system engendered by binary
nonlinearization is reduced to a specific involutive system generated by
mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento
A new extended q-deformed KP hierarchy
A method is proposed in this paper to construct a new extended q-deformed KP
(-KP) hiearchy and its Lax representation. This new extended -KP
hierarchy contains two types of q-deformed KP equation with self-consistent
sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey
hierarchy with self-consistent sources and the constrained q-deformed KP
hierarchy, which include two types of q-deformed KdV equation with sources and
two types of q-deformed Boussinesq equation with sources. All of these results
reduce to the classical ones when goes to 1. This provides a general way to
construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with
sources and their Lax representations.Comment: 17 pages, no figur
Endogenous aldehyde accumulation generates genotoxicity and exhaled biomarkers in esophageal adenocarcinoma
Volatile aldehydes are enriched in esophageal adenocarcinoma (EAC) patients’ breath and could improve early diagnosis, however the mechanisms of their production are unknown. Here, we show that weak aldehyde detoxification characterizes EAC, which is sufficient to cause endogenous aldehyde accumulation in vitro. Two aldehyde groups are significantly enriched in EAC biopsies and adjacent tissue: (i) short-chain alkanals, and (ii) medium-chain alkanals, including decanal. The short-chain alkanals form DNA-adducts, which demonstrates genotoxicity and confirms inadequate detoxification. Metformin, a putative aldehyde scavenger, reduces this toxicity. Tissue and breath concentrations of the medium-chain alkanal decanal are correlated, and increased decanal is linked to reduced ALDH3A2 expression, TP53 deletion, and adverse clinical features. Thus, we present a model for increased exhaled aldehydes based on endogenous accumulation from reduced detoxification, which also causes therapeutically actionable genotoxicity. These results support EAC early diagnosis trials using exhaled aldehyde analysis
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