2063 research outputs found
Sort by
Exploiting the Kronecker product structure of φ−functions in exponential integrators
Get PDFExponential time integrators are well-established discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related to the exponential. This work introduces an algorithm to speed up the computation of the (Formula presented.) function action over vectors for two-dimensional (2D) matrices expressed as a Kronecker sum. For that, we present an auxiliary exponential-related matrix function that we express using Kronecker products of one-dimensional matrices. We exploit state-of-the-art implementations of (Formula presented.) functions to compute this auxiliary function's action and then recover the original (Formula presented.) action by solving a Sylvester equation system. Our approach allows us to save memory and solve exponential integrators of 2D+time problems in a fraction of the time traditional methods need. We analyze the method's performance considering different linear operators and with the nonlinear 2D+time Allen–Cahn equation
The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition
Get PDFThis paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition and a volume constraint. We establish in 2D the existence of an optimal shape that has two cusps on the boundary. We also prove the boundary of the droplet is a chord-arc curve with its normal vector field in the VMO space, and its arc-length parametrization belongs to the Sobolev space . In fact, the boundary curves of such droplets closely resemble the so-called Weil-Petersson class of planar curves. In addition, the asymptotic behavior of the optimal shape when the volume becomes extremely large or small is also studied
Wigner's friends, tunnelling times and Feynman's "only mystery of quantum mechanics"
Get PDFRecent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery".ELKARTEK
KK-2021/00064;
KK-2021/00022;
KK-2020/0000
Combined model-based and machine learning approach for damage identification in bridge type structures
Get PDFIn this work, we propose a combined approach of model-based and machine learning techniques for damage identification in bridge structures. First, a finite element model is calibrated with real data from experimental vibration modes for the undamaged or baseline state. Second, generic synthetic damage scenarios based on modal parameters are automatically generated with the model to train machine learning algorithms for damage classification (Support Vector Machine, SVM) and damage location and quantification (Neural Network, NN). For an initial validation of the method we use a lab scale truss bridge model, proving that specific damage scenarios can be assessed by the Supervised Machine Learning algorithms trained with generic damage scenarios including a certain variability. The NN provides an assessment in terms of damage location and quantification, whereas the SVM provides a damage severity classification with graphical indication of the damage location and quantification through a reduced dimension plot
On the advection-diffusion equation with rough coefficients: Weak solutions and vanishing viscosity
Get PDFWe deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergence-free vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme to the unique Lagrangian solution of the transport equation. Our proof is based on the use of stochastic flows and yields quantitative rates of convergence. This offers a completely general selection criterion for the transport equation (even beyond the distributional regime) which compensates the wild non-uniqueness phenomenon for solutions with low integrability arising from convex integration constructions, as shown in recent works [8,28–30], and rules out the possibility of anomalous dissipation.ERC Starting Grant 676675 FLIRT, ERC Starting Grant 757254 SINGULARITY, ERC Starting Grant 101039762 HamDyWW
Asymptotic behavior of the interface for entire vector minimizers in phase transitions
Get PDFWe study globally bounded entire minimizers of Allen-Cahn systems for potentials with and near , . Such solutions are, over large regions, identically equal to some zeroes of the potential 's. We establish the estimates
for the diffuse interface and the free boundary . Furthermore, if we establish the upper bound
\mathcal{H}^{n-1}(\partial^* I_0\cap B_r(x_0))\leq c_3r^{n-1}, \quad r\geq r_0(x_0).
$
Effects of random inputs and short-term synaptic plasticity in a LIF conductance model for working memory applications
Get PDFWorking memory (WM) has been intensively used to enable
the temporary storing of information for processing purposes, playing an
important role in the execution of various cognitive tasks. Recent studies
have shown that information in WM is not only maintained through persistent recurrent activity but also can be stored in activity-silent states
such as in short-term synaptic plasticity (STSP). Motivated by important applications of the STSP mechanisms in WM, the main focus of the
present work is on the analysis of the effects of random inputs on a leaky
integrate-and-fire (LIF) synaptic conductance neuron under STSP. Furthermore, the irregularity of spike trains can carry the information about
previous stimulation in a neuron. A LIF conductance neuron with multiple inputs and coefficient of variation (CV) of the inter-spike-interval
(ISI) can bring an output decoded neuron. Our numerical results show
that an increase in the standard deviations in the random input current
and the random refractory period can lead to an increased irregularity
of spike trains of the output neuron
Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications
Get PDFPopulation dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for
many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding
problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains.
We propose a model based on a coupled system of reflecting Skorokhod-type stochastic differential equations with jump-like exit from
a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use
compactness methods and Skorokhod’s representation of solutions to SDEs posed in bounded domains to prove the well-posedness
of the system. This functional setting is a new point of view in the field of modelling and simulation of population dynamics. We
provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson-Cowan-type
system, modelling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of
random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems
Performance measures of nonstationary inventory models for perishable products under the EWA policy
Get PDFAccurately estimating key performance indicators in inventory models for perishable items is essential
in order to assess and improve the management strategy of these systems. We analyse the production
of platelet concentrates at blood banks under the EWA replenishment policy. We give analytical
approximations of the most important performance measures, such as the size of orders, the size of
stocks, the percentage of outdating, the age distribution of stocks and the freshness of units issued,
among others. The production of platelet concentrates is a prototypical example of inventory models
for short life items with random demand and a weekly pattern, where a high service level is required.
The methodology and the approximations presented here can be easily adapted to other inventory
systems with similar characteristics. Most of the formulae in this article are new for nonstationary
models under the EWA policy; indeed, formulae for the age distribution of units in stock and of
units issued have not appeared in the literature even for the simpler base-stock replenishment policy.
We apply our results to a real blood bank and find very close agreement between the formulae and
the results of Monte Carlo simulations. The accuracy of our approximations is also tested in several
scenarios, depending on the lifetime of units, safety stock levels and the probabilistic distribution of
demand.PID2020-116873GB-I0
Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit
No full textWe consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular case. We build on previous work on understanding the behaviour of such models within the large-domain limit, where minimisers converge to minimisers of a quadratic elastic energy with manifold-valued constraint, analogous to harmonic maps. We extend this work to establish Hölder bounds for (almost-)minimisers on bounded domains, and demonstrate stronger convergence of (almost)-minimisers away from the singular set of the limit solution. The proof techniques bear analogy with recent work of singularly perturbed energy functionals, in particular in the context of the Ginzburg–Landau and Landau–de Gennes models