2,942 research outputs found
On quantization of r-matrices for Belavin-Drinfeld Triples
We suggest a formula for quantum universal -matrices corresponding to
quasitriangular classical -matrices classified by Belavin and Drinfeld for
all simple Lie algebras. The -matrices are obtained by twisting the standard
universal -matrix.Comment: 12 pages, LaTe
Lipidic Formulations Inspired by COVID Vaccines as Smart Coatings to Enhance Nanoparticle-Based Cancer Therapy
Recent advances in nanomedicine have led to the introduction and subsequent establishment of nanoparticles in cancer treatment and diagnosis. Nonetheless, their application is still hindered by a series of challenges related to their biocompatibility and biodistribution. In this paper, we take inspiration from the recently produced and widely spread COVID vaccines, based on the combinational use of ionizable solid lipid nanoparticles, cholesterol, PEGylated lipids, and neutral lipids able to incorporate mRNA fragments. Here, we focus on the implementation of a lipidic formulation meant to be used as a smart coating of solid-state nanoparticles. The composition of this formulation is finely tuned to ensure efficient and stable shielding of the cargo. The resulting shell is a highly customized tool that enables the possibility of further functionalizations with targeting agents, peptides, antibodies, and fluorescent moieties for future in vitro and in vivo tests and validations. Finally, as a proof of concept, zinc oxide nanoparticles doped with iron and successively coated with this lipidic formulation are tested in a pancreatic cancer cell line, BxPC-3. The results show an astonishing increase in cell viability with respect to the same uncoated nanoparticles. The preliminary results presented here pave the way towards many different therapeutic approaches based on the massive presence of highly biostable and well-tolerated nanoparticles in tumor tissues, such as sonodynamic therapy, photodynamic therapy, hyperthermia, and diagnosis by means of magnetic resonance imaging
Quantum Lie algebras associated to and
Quantum Lie algebras \qlie{g} are non-associative algebras which are
embedded into the quantized enveloping algebras of Drinfeld and Jimbo
in the same way as ordinary Lie algebras are embedded into their enveloping
algebras. The quantum Lie product on \qlie{g} is induced by the quantum
adjoint action of . We construct the quantum Lie algebras associated to
and . We determine the structure constants and the
quantum root systems, which are now functions of the quantum parameter .
They exhibit an interesting duality symmetry under .Comment: Latex 9 page
Representations of the quantum matrix algebra
It is shown that the finite dimensional irreducible representaions of the
quantum matrix algebra ( the coordinate ring of ) exist only when both q and p are roots of unity. In this case th e space of
states has either the topology of a torus or a cylinder which may be thought of
as generalizations of cyclic representations.Comment: 20 page
A mean-field kinetic lattice gas model of electrochemical cells
We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate
electrochemical cells. We start from a microscopic lattice-gas model with
charged particles, and build mean-field kinetic equations following the lines
of earlier work for neutral particles. We include the Poisson equation to
account for the influence of the electric field on ion migration, and
oxido-reduction processes on the electrode surfaces to allow for growth and
dissolution. We confirm the viability of our approach by simulating (i) the
electrochemical equilibrium at flat electrodes, which displays the correct
charged double-layer, (ii) the growth kinetics of one-dimensional
electrochemical cells during growth and dissolution, and (iii) electrochemical
dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure
On Quantum Lie Algebras and Quantum Root Systems
As a natural generalization of ordinary Lie algebras we introduce the concept
of quantum Lie algebras . We define these in terms of certain
adjoint submodules of quantized enveloping algebras endowed with a
quantum Lie bracket given by the quantum adjoint action. The structure
constants of these algebras depend on the quantum deformation parameter and
they go over into the usual Lie algebras when .
The notions of q-conjugation and q-linearity are introduced. q-linear
analogues of the classical antipode and Cartan involution are defined and a
generalised Killing form, q-linear in the first entry and linear in the second,
is obtained. These structures allow the derivation of symmetries between the
structure constants of quantum Lie algebras.
The explicitly worked out examples of and illustrate the
results.Comment: 22 pages, latex, version to appear in J. Phys. A. see
http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further
informatio
On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media
The fluctuations of the jamming coverage upon Random Sequential Adsorption
(RSA) are studied using both analytical and numerical techniques. Our main
result shows that these fluctuations (characterized by )
decay with the lattice size according to the power-law . The exponent depends on the dimensionality of
the substrate and the fractal dimension of the set where the RSA process
actually takes place () according to .This
theoretical result is confirmed by means of extensive numerical simulations
applied to the RSA of dimers on homogeneous and stochastic fractal substrates.
Furthermore, our predictions are in excellent agreement with different previous
numerical results.
It is also shown that, studying correlated stochastic processes, one can
define various fluctuating quantities designed to capture either the underlying
physics of individual processes or that of the whole system. So, subtle
differences in the definitions may lead to dramatically different physical
interpretations of the results. Here, this statement is demonstrated for the
case of RSA of dimers on binary alloys.Comment: 20 pages, 8 figure
Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
We reveal a phase transition with decreasing viscosity at \nu=\nu_c>0
in one-dimensional decaying Burgers turbulence with a power-law correlated
random profile of Gaussian-distributed initial velocities
\sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian
one-point probability density of velocities, continuously dependent on \nu,
reflecting a spontaneous one step replica symmetry breaking (RSB) in the
associated statistical mechanics problem. We obtain the low orders cumulants
analytically. Our results, which are checked numerically, are based on
combining insights in the mechanism of the freezing transition in random
logarithmic potentials with an extension of duality relations discovered
recently in Random Matrix Theory. They are essentially non mean-field in nature
as also demonstrated by the shock size distribution computed numerically and
different from the short range correlated Kida model, itself well described by
a mean field one step RSB ansatz. We also provide some insights for the finite
viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6
pages, 5 figure
Universal integrability objects
We discuss the main points of the quantum group approach in the theory of
quantum integrable systems and illustrate them for the case of the quantum
group . We give a complete set of the
functional relations correcting inexactitudes of the previous considerations. A
special attention is given to the connection of the representations used to
construct the universal transfer operators and -operators.Comment: 21 pages, submitted to the Proceedings of the International Workshop
"CQIS-2012" (Dubna, January 23-27, 2012
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