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Robust Variational Physics-Informed Neural Networks
Get PDFWe introduce a Robust version of the Variational Physics-Informed Neural Networks method (RVPINNs).
As in VPINNs, we define the quadratic loss functional in terms of a Petrov-Galerkin-type variational formulation
of the PDE problem: the trial space is a (Deep) Neural Network (DNN) manifold, while the test space is a
finite-dimensional vector space. Whereas the VPINN’s loss depends upon the selected basis functions of a given
test space, herein, we minimize a loss based on the discrete dual norm of the residual. The main advantage of
such a loss definition is that it provides a reliable and efficient estimator of the true error in the energy norm
under the assumption of the existence of a local Fortin operator. We test the performance and robustness of our
algorithm in several advection-diffusion problems. These numerical results perfectly align with our theoretical
findings, showing that our estimates are sharp
The impact of Mn and Al on the trapping and diffusion of hydrogen in γ-Fe: An atomistic insight
No full textCommon alloying elements such as Mn and Al can significantly influence the local dynamics of Hydrogen in steel, promoting or attenuating the mechanisms associated with Hydrogen induced Embrittlement (HIE). Here, we propose a first principles-based framework to systematically unlock the physical underpinnings of such influence in Mn/Al-alloyed γ-Fe. Our framework can be readily adapted to analyse H behaviour in the bulk phase of any face-centred cubic (FCC) Fe-X-Y alloy, provided that solutes X and Y substitute the Fe sites. In our scheme, all thermodynamically stable substitutional solute sites were identified ( ≤ 5.4 wt% Mn; ≤ 4 wt% Al) up to the third nearest neighbour (NN) shell of a single H atom. The impact of Mn/Al on H-binding was quantitatively evaluated, indicating a surprisingly strong correlation with the local Al distribution regardless Mn content, and indirect stabilization by Al when present in the 2nd NN shell. Nonetheless, Al strongly repels H bonding. The contradictory role of Al was explained in terms of bonding/anti-bonding orbitals occupancy in H-M interactions (M = Al, Mn, Fe). The barriers to H hopping between adjacent local environments and the corresponding jump frequencies were subsequently calculated, providing insights into the limits imposed by the presence of Al and Mn on H mobility in Mn/Al-alloyed γ-Fe. Most notably, presence of Al in the 2nd NN shell of H severely reduces the H jump frequency, leading to irreversible trapping at Al high contents. Such behaviour may critically contribute to mitigate H-induced delayed fracture in Al-rich austenite steel.JDC2022-049793-I/MCIN/AEI/10.13039/501100011033
RyC2022-036500-I
CEX2021-001142-S
PID2022-136585NB-C22
RES, QHS-2023-2-003
Prey group defense and hunting cooperation among generalist-predators induce complex dynamics: a mathematical study
No full textGroup defense in prey and hunting cooperation in predators are two important ecological phenomena and can occur concurrently. In this article, we consider cooperative hunting in generalist predators and group defense in prey under a mathematical framework to comprehend the enormous diversity the model could capture. To do so, we consider a modified Holling-Tanner model where we implement Holling type IV functional response to characterize grazing pattern of predators where prey species exhibit group defense. Additionally, we allow a modification in the attack rate of predators to quantify the hunting cooperation among them. The model admits three boundary equilibria and up to three coexistence equilibrium points. The geometry of the nontrivial prey and predator nullclines and thus the number of coexistence equilibria primarily depends on a specific threshold of the availability of alternative food for predators. We use linear stability analysis to determine the types of hyperbolic equilibrium points and characterize the non-hyperbolic equilibrium points through normal form and center manifold theory. Change in the model parameters leading to the occurrences of a series of local bifurcations from non-hyperbolic equilibrium points, namely, transcritical, saddle-node, Hopf, cusp and Bogdanov-Takens bifurcation; there are also occurrences of global bifurcations such as homoclinic bifurcation and saddle-node bifurcation of limit cycles. We observe two interesting closed ‘bubble’ form induced by global bifurcations due to change in the strength of hunting cooperation and the availability of alternative food for predators. A three dimensional bifurcation diagram, concerning the original system parameters, captures how the alternation in model formulation induces gradual changes in the bifurcation scenarios. Our model highlights the stabilizing effects of group or gregarious behaviour in both prey and predator, hence supporting the predator-herbivore regulation hypothesis. Additionally, our model highlights the occurrence of “saltatory equilibria" in ecological systems and capture the dynamics observed for lion-herbivore interactions
Stability and deformation of F-singularities
No full textWe study the problem of m-adic stability of F-singularities, that is, whether the property that a quotient of a local ring (R,m) by a non-zero divisor x∈m has good F-singularities is preserved in a sufficiently small m-adic neighborhood of x. We show that m-adic stability holds for F-rationality in full generality, and for F-injectivity, F-purity and strong F-regularity under certain assumptions. We show that strong F-regularity and F-purity are not stable in general. Moreover, we exhibit strong connections between stability and deformation phenomena, which hold in great generality.La Caixa Postdoctoral Junior Leader,
Ramon y Cajal RYC2020-028976-
COMPACT CONTACT SETS OF SUB-QUADRATIC SOLUTIONS TO THE THIN OBSTACLE PROBLEM
No full textWe study global solutions to the thin obstacle problem with at
most quadratic growth at infinity.
We show that every ellipsoid can be realized as the contact set of such a
solution. On the other hand, if such a solution has a compact contact set, we
show that it must be an ellipsoid
SUFFICIENT CONDITIONS FOR THE EXISTENCE OF MINIMIZING HARMONIC MAPS WITH AXIAL SYMMETRY IN THE SMALL-AVERAGE REGIME
No full textThe paper concerns the analysis of global minimizers of a Dirichlet-type en-
ergy functional defined on the space of vector fields H1(S, T ), where S and T are surfaces
of revolution. The energy functional we consider is closely related to a reduced model
in the variational theory of micromagnetism for the analysis of observable magnetization
states in curved thin films. We show that axially symmetric minimizers always exist,
and if the target surface T is never flat, then any coexisting minimizer must have line
symmetry. Thus, the minimization problem reduces to the computation of an optimal
one-dimensional profile. We also provide a necessary and sufficient condition for energy
minimizers to be axially symmetric
Interaction energies in paranematic colloids
No full textWe consider a system of colloidal particles embedded in a paranematic—an isotropic
phase of a nematogenic medium above the temperature of the nematic-to-isotropic tran-
sition. In this state, the nematic order is induced by the boundary conditions in a narrow
band around each particle and it decays exponentially in the bulk.
We develop rigorous asymptotics of the linearization of the appropriate variational
model that allow us to describe weak far-field interactions between the colloidal par-
ticles in two dimensional paranematic suspensions. We demonstrate analytically that
decay rates of solutions to the full nonlinear and linear problems are similar and verify
numerically that the interactions between the particles in these problems have similar
dependence on the distance between the particles. Finally, we perform Monte-Carlo
simulations for a system of colloidal particles in a paranematic and describe the statis-
tical properties of this system
Limited Visual Range in the Social Force Model: Effects on Macroscopic and Microscopic Dynamics
Get PDFThe Social Force Model has been widely used to simulate pedestrian dynamics. Its simplicity and ability to reproduce some collective patterns of behavior make it an adequate tool in the field of pedestrian dynamics. However, its ability to reproduce common macroscopic empirical results, such as pedestrian flows through a bottleneck and the speed-density fundamental diagram, has scarcely been studied. In addition, the effect of each parameter of the model on the dynamics of the system has rarely been shown. In this contribution, a comprehensive parameter-sensitivity analysis in the social force model is provided, and an optimal set is introduced, capable of reproducing both macroscopic experimental flow data and collision avoidance between pedestrians in simple trajectories on the microscopic scale. We show that the incorporation of asymmetric visual range models in the inter-pedestrian
interactions is required for quantitative agreement. The model is also capable of showing collision avoidance in simple pedestrian trajectories and lane formation in non-crowded bidirectional pedestrian flows
An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
Get PDFA curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ, ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs.BERC 2022-2025
Severo Ochoa CEX2021-001142-S / MCIN / AEI / 10.13039/50110001103
A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion
Get PDFThis paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented