3,429 research outputs found
Exponential number of equilibria and depinning threshold for a directed polymer in a random potential
By extending the Kac-Rice approach to manifolds of finite internal dimension,
we show that the mean number
of all possible equilibria
(i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line
(directed polymer), confined in a harmonic well and submitted to a quenched
random Gaussian potential in dimension , grows exponentially
with its
length . The growth rate is found to be directly related to the
generalised Lyapunov exponent (GLE) which is a moment-generating function
characterising the large-deviation type fluctuations of the solution to the
initial value problem associated with the random Schr\"odinger operator of the
1D Anderson localization problem. For strong confinement, the rate is small
and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to
GLE. For weak confinement, the rate is found to be proportional to the
inverse Larkin length of the pinning theory. As an application, identifying the
depinning with a landscape "topology trivialization" phenomenon, we obtain an
upper bound for the depinning threshold , in the presence of an applied
force, for elastic lines and -dimensional manifolds, expressed through the
mean modulus of the spectral determinant of the Laplace operators with a random
potential. We also discuss the question of counting of stable equilibria.
Finally, we extend the method to calculate the asymptotic number of equilibria
at fixed energy (elastic, potential and total), and obtain the (annealed)
distribution of the energy density over these equilibria (i.e. force-free
configurations). Some connections with the Larkin model are also established.Comment: v1: 6 pages main text + 14 pages supplemental material, 10 figures.
v2: LaTeX, 79 pages, 18 eps figures, new material (Sections 6, 10, 11 &
Appendices C, E, F, G
Biomimicking Extracellular Vesicles with Fully Artificial Ones: A Rational Design of EV-BIOMIMETICS toward Effective Theranostic Tools in Nanomedicine
Extracellular Vesicles (EVs) are the protagonists in cell communication and membrane trafficking, being responsible for the delivery of innumerable biomolecules and signaling moieties. At the moment, they are of paramount interest to researchers, as they naturally show incredibly high efficiency and specificity in delivering their cargo. For these reasons, EVs are employed or inspire the development of nanosized therapeutic delivery systems. In this Perspective, we propose an innovative strategy for the rational design of EV-mimicking vesicles (EV-biomimetics) for theranostic scopes. We first report on the current state-of-the-art use of EVs and their byproducts, such as surface-engineered EVs and EV-hybrids, having an artificial cargo (drug molecule, genetic content, nanoparticles, or dye incorporated in their lumen). Thereafter, we report on the new emerging field of EV-mimicking vesicles for theranostic scopes. We introduce an approach to prepare new, fully artificial EV-biomimetics, with particular attention to maintaining the natural reference lipidic composition. We overview those studies investigating natural EV membranes and the possible strategies to identify key proteins involved in site-selective natural homing, typical of EVs, and their cargo transfer to recipient cells. We propose the use also of molecular simulations, in particular of machine learning models, to approach the problem of lipid organization and self-assembly in natural EVs. We also discuss the beneficial feedback that could emerge combining the experimental tests with atomistic and molecular simulations when designing an EV-biomimetics lipid bilayer. The expectations from both research and industrial fields on fully artificial EV-biomimetics, having the same key functions of natural ones plus new diagnostic or therapeutic functions, could be enormous, as they can greatly expand the nanomedicine applications and guarantee on-demand and scalable production, off-the-shelf storage, high reproducibility of morphological and functional properties, and compliance with regulatory standards
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
Short time relaxation of a driven elastic string in a random medium
We study numerically the relaxation of a driven elastic string in a two
dimensional pinning landscape. The relaxation of the string, initially flat, is
governed by a growing length separating the short steady-state
equilibrated lengthscales, from the large lengthscales that keep memory of the
initial condition. We find a macroscopic short time regime where relaxation is
universal, both above and below the depinning threshold, different from the one
expected for standard critical phenomena. Below the threshold, the zero
temperature relaxation towards the first pinned configuration provides a novel,
experimentally convenient way to access all the critical exponents of the
depinning transition independently.Comment: 4.2 pages, 3 figure
Factors affecting the vaccination choices of pregnant women for their children. A systematic review of the literature
In recent years, an increase in vaccine hesitancy has led to a decrease in vaccination coverage in several countries. We conducted a systematic review of studies that assessed knowledge of and attitudes toward pediatric vaccinations, and the vaccination choices and their determinants among pregnant women. A total of 6,277 records were retrieved, and 16 full texts were included in the narrative synthesis. The published literature on the topic shows that, overall, pregnant women believe that vaccines are important for the protection of their children and the community, but various concerns and misunderstandings persist around vaccine safety and efficacy, which reduce the trust of expectant mothers in immunization. Nevertheless, such attitudes and choices vary depending on the vaccine being considered and the corresponding determinants should therefore be studied in the context of each specific vaccination. Further research on this topic is needed, particularly in non-western countries
Free-energy distribution of the directed polymer at high temperature
We study the directed polymer of length in a random potential with fixed
endpoints in dimension 1+1 in the continuum and on the square lattice, by
analytical and numerical methods. The universal regime of high temperature
is described, upon scaling 'time' and space (with for the discrete model) by a continuum model with
-function disorder correlation. Using the Bethe Ansatz solution for the
attractive boson problem, we obtain all positive integer moments of the
partition function. The lowest cumulants of the free energy are predicted at
small time and found in agreement with numerics. We then obtain the exact
expression at any time for the generating function of the free energy
distribution, in terms of a Fredholm determinant. At large time we find that it
crosses over to the Tracy Widom distribution (TW) which describes the fixed
infinite limit. The exact free energy distribution is obtained for any time
and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to
Tracy Widom established, 1 figure changed
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
Vapor pressure measurements over supercooled water in the temperature range from −10 1 °C to +10 −2 °C
An accurate measurement of saturation vapor pressure of supercooled water is a strong challenge in
metrology, mainly due to difficulties concerning keeping water at a liquid state at temperatures well
below the melting point; thus few experimental data covering limited temperature ranges (down to
about 253 K) are reported in literature. For this reason, an investigation of the water vapor – supercooled
water equilibrium along the saturation line is carried out at Istituto Nazionale di Ricerca Metrologica
(INRIM).
Measurements cover the temperature range from 261.26 K to 273.25 K, corresponding to a saturation
vapor pressure from about 244 Pa to 611 Pa. The experimental apparatus includes a borosilicate glass
sample cell, kept in a liquid bath at a constant temperature with millikelvin stability and connected to
a manifold where the pressure is measured using a capacitive diaphragm pressure gauge.
In this work, the water sample preparation, the measuring method and measurement corrections are
reported; moreover, a comparison between experimental and literature data is conducted along with
the most used vapor pressure formulations. Measurement results are discussed and uncertainty sources
estimated. The resulting expanded relative uncertainty (k = 2) varies from 0.085% at 261.26 K to 0.039% at
273.25 K
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