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Well-posedness theory for non-homogeneous incompressible fluids with odd viscosity
Get PDFSeveral fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum
and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed “odd viscosity”, becomes non-dissipative. At
the mathematical level, this fact translates into a loss of derivatives at the level of a priori estimates: while the odd viscosity term
depends on derivatives of the velocity field, no parabolic smoothing effect can be expected.
In the present paper, we establish a well-posedness theory in Sobolev spaces for a system of incompressible non-homogeneous
fluids with odd viscosity. The crucial point of the analysis is the introduction of a set of good unknowns, which allow for the
emerging of a hidden hyperbolic structure underlying the system of equations. It is exactly this hyperbolic structure which makes
it possible to circumvent the derivative loss and propagate high enough Sobolev norms of the solution. The well-posedness result
is local in time; two continuation criteria are also established
Bifurcation analysis of a two infection SIR-SIR epidemic model with temporary immunity and disease enhancement
No full textIn this paper we study a two infection SIR-SIR compartmental model, considering biological features described in dengue fever epidemiology. Due to a progressive loss of protective antibodies there is waning immunity in the first infection stage and disease enhancement or protection effects by the second infection stage. Bifurcation analysis reveals two codim-2 bifurcations as organizing centers. The unfolding of a cusp bifurcation describes the transition of the disease-free equilibrium into an endemic equilibrium by varying a parameter. These equilibria allow an analytical solution with explicit expressions which allow for a full geometrical interpretation of the occurring bifurcations related to stationary dynamics. A Bogdanov-Takens point is the starting point in the parameter space where oscillatory endemic dynamics occurs including a homoclinic connection. These findings bring additional insights on biological mechanisms able to generate rich and complicated dynamical behavior in simple epidemic models that are, so far, largely unexplored.M.A. acknowledges the financial support by the Min-
isterio de Ciencia e Innovacion (MICINN) of the Spanish Gov-
ernment through the Ramon y Cajal Grant RYC2021-031380-
I funded by MICIU/AEI/10.13039/501100011033 and by the
European Union extGenerationEU/ PRTR. A.K.S. acknowl-
edged the financial support by the ministerio de ciencia e
innovación (MICINN) of the Spanish Government through
the juan de la cierva grant FJC-2021-046826-I /MICIU/AEI
/10.13039/501100011033 y por la Unión Europea NextGenera-
tionEU/ PRTR
On the effect of a large cloud of rigid particles on the motion of an incompressible non–Newtonian fluid
No full textWe show that the collective effect of N rigid bodies (Sn,N)N
n of diameters (rn,N)N
n immersed in
an incompressible non–Newtonian fluid is negligible in the asymptotic limit N → ∞ as long as their
total packing volume N
n rd
n,N, d = 2, 3 tends to zero exponentially – N
n rd
n,N ≈ A N – for a
certain constant A > 1. The result is rather surprising and in a sharp contrast with the associated
homogenization problem, where the same number of obstacles can completely stop the fluid motion in
the case of shear thickening viscosity. A large class of non–Newtonian fluids is included, for which the
viscous stress is a subdifferential of a convex potential
Monitoring Alzheimer's disease via ultraweak photon emission
No full textIn an innovative experiment, we detected ultraweak photon emission (UPE) from the hippocampus of male rat brains and found significant correlations between Alzheimer's disease (AD), memory decline, oxidative stress, and UPE intensity. These findings may open up novel methods for screening, detecting, diagnosing, and classifying neurodegenerative diseases, particularly AD. The study suggests that UPE from the brain's neural tissue can serve as a valuable indicator. It also proposes the development of a minimally invasive brain-computer interface (BCI) photonic chip for monitoring and diagnosing AD, offering high spatiotemporal resolution of brain activity. The study used a rodent model of sporadic AD, demonstrating that STZ-induced sAD resulted in increased hippocampal UPE, which was associated with oxidative stress. Treatment with donepezil reduced UPE and improved oxidative stress. These findings support the potential utility of UPE as a screening and diagnostic tool for AD and other neurodegenerative diseases.RTI2018-093860-B-C21 funded by (AEI/FEDER, UE) and acronym ‘‘MathNEURO’’;
grant (No. 22112) from Shiraz University of Medical Sciences, Shiraz, Iran;
Natural Sciences and Engineering Research Council of Canada (NSERC) of Canada, the National Research Council (NRC) of Canada, and the New Frontiers in Research Fund (NFRF) a program by the Social Sciences and Humanities Research Council (SSHRC), Canada
Large-scale unsupervised spatio-temporal semantic analysis of vast regions from satellite images sequences
Get PDFTemporal sequences of satellite images constitute a highly valuable and abundant resource for analyzing regions of interest. However, the automatic acquisition of knowledge on a large scale is a challenging task due to different factors such as the lack of precise labeled data, the definition and variability of the terrain entities, or the inherent complexity of the images and their fusion. In this context, we present a fully unsupervised and general methodology to conduct spatio-temporal taxonomies of large regions from sequences of satellite images. Our approach relies on a combination of deep embeddings and time series clustering to capture the semantic properties of the ground and its evolution over time, providing a comprehensive understanding of the region of interest. The proposed method is enhanced by a novel procedure specifically devised to refine the embedding and exploit the underlying
spatio-temporal patterns. We use this methodology to conduct an in-depth analysis of a 220 km2 region in northern Spain in different settings. The results provide a broad and intuitive perspective of the land where large areas are connected in a compact and well-structured manner, mainly based on climatic, phytological, and hydrological factors
Smoothed Particle Hydrodynamics simulations of integral multi-mode and fractional viscoelastic models
No full textTo capture specific characteristics of non-Newtonian fluids, during the past years fractional constitutive models have become increasingly popular. These models are able to capture, in a simple and compact way, the complex behaviour of viscoelastic materials, such as the change in power-law relaxation pattern during the relaxation process of some materials. Using the Lagrangian Smoothed-Particle Hydrodynamics (SPH) method we can easily track particle history; this allows us to solve integral constitutive models in a novel way, without relying on complex tasks. Hence, we develop here a SPH integral viscoelastic method which is first validated for simple Maxwell or Oldroyd-B models under Small Amplitude Oscillatory Shear (SAOS) and start-up channel flows. By exploiting the structure of the integral method, a multi-mode Maxwell model is then implemented. Finally, the method is extended to include fractional constitutive models, validating the approach by comparing results with theory
Development of methods based on neural networks in the estimation of mineral resources
Get PDFDebido a limitaciones económicas y físicas, nuestra comprensión de los
recursos minerales en un área de interés específica es limitada y
fragmentada. Tradicionalmente, este problema se ha resuelto utilizando el
método geoestadístico de Kriging, donde la ley del mineral se estima en
ubicaciones sin mediciones utilizando valores conocidos de la ley en
puntos circundantes. La ventaja de este método radica en el cálculo de
pesos a través de un modelo de variabilidad espacial conocido como
variograma. Sin embargo, su desventaja es que se basa en el supuesto
de estacionariedad, aditividad, linealidad y de cierta forma el modelado
variográfico es subjetivo. Este estudio propone abordar el problema de
estimación de recursos minerales como un problema de regresión
utilizando redes neuronales, que no están sujetas a las restricciones de
estacionariedad, aditividad, linealidad y modelado espacial de los métodos
geoestadísticos. Se han comparado el Kriging y una red neuronal de
función de base radial y un perceptrón multicapa utilizando distintas
métricas de validación. Los resultados muestran que un modelo de red
neuronal adecuadamente entrenado, con un etiquetado apropiado de la
ley mineral y sus características de entrada, logra resultados similares al
enfoque geoestadístico con una reducción de tiempo significativo,
evitando a su vez todos los supuestos antes señalados. Sin embargo, las
redes neuronales no consideran la correlación espacial de la ley del
mineral ni la reproducen en los lugares donde se midió, características que
han marcado desconfianza en su implementación industrial y que se
discuten en este artículo proponiendo finalmente un ajuste entre ambos
enfoques a un mínimo sacrificio del coste temporal y de mano de obra
Complex Network Approaches for Epidemic Modeling: A Case Study of COVID-19
Get PDFSince the SARS-CoV-2 outbreak, the importance of mathematical modeling as a tool for comprehending disease dynamics has been highlighted, with several mathematical modeling techniques being applied and developed to simulate and measure the impact of interventions aimed at controlling the spread of the disease and minimizing its burden. In this work, we applied complex network techniques to analyze a Susceptible-Exposed-Asymptomatic-Hospitalized-Recovered (SEAHR) model to describe COVID-19 transmission dynamics, using the Basque Country region of Spain as a case study. We compared two network modeling approaches: the Watts-Strogatz network and the Barabasi-Albert scale-free network. By applying immunization strategies on both networks, we demonstrate that targeted immunization yields superior results within a scale-free network due to its increased heterogeneity. Moreover, the basic reproduction number of the model is calculated, and sensitivity analysis is performed to determine the influence of the model parameters on the disease dynamics.Juan de la Cierva Formación grant FJC2021-046826-I
A numerical algorithm for the computation of the noncentral beta distribution function
No full textThe noncentral beta distribution function is a generalization of the central beta distribu-
tion (the regularized incomplete beta function) that includes a noncentrality parameter.
This paper describes an algorithm and provides a Matlab implementation for calcu-
lating the noncentral beta distribution function. Through a series of numerical tests,
we demonstrate that the algorithm is accurate and efficient across a wide range of
parameters
