Browsing by Author "Petrache, Mircea"

Now showing 1 - 14 of 14
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    Almost Sure Recovery in Quasi-periodic Structures
    (2023) Petrache, Mircea; Viera, Rodolfo
    We study random perturbations of quasi-periodic uniformly discrete sets in the d-dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set X can be almost surely recovered from its random perturbations. This extends the recent periodic case result of Yakir (Int Math Res Notices 1-19, 2020).
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    CLASSIFICATION OF UNIFORMLY DISTRIBUTED MEASURES OF DIMENSION 1 IN GENERAL CODIMENSION
    (2021) Laurain, Paul; Petrache, Mircea
    Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in R-d has remained open, except. for d = 1 and for compactly supported measures in d = 2, and for codimension 1. In this paper we study 1-dimensional measures in R-d for all d and classify uniform measures with connected 1-dimensional support, which turn out to be homogeneous measures. We provide as well a partial classification of general uniform measures of dimension 1 in the absence of the connected support hypothesis.
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    Coefficient Groups Inducing Nonbranched Optimal Transport
    (2018) Petrache, Mircea; Zust, Roger
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    Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings
    (2022) Del Nin, Giacomo; Petrache, Mircea
    We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in this way. Exploiting the "multigrid construction" of quasiperiodic tilings (which is an extension of De Bruijn's "pentagrid" construction of Penrose tilings) we adapt the same techniques to also find the macroscopical homogenized perimeter when we microscopically rescale a given quasiperiodic tiling.
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    Corrigendum to "Asymptotics for the Unconstrained Polarization (Chebyshev) Problem"
    (2023) Hardin, Douglas; Petrache, Mircea; Saff, Edward B.
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    Crystallization to the Square Lattice for a Two-Body Potential
    (2021) Betermin, Laurent; De Luca, Lucia; Petrache, Mircea
    We consider two-dimensional zero-temperature systems of N particles towhich we associate an energy of the form
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    Existence and Uniqueness of Monge Minimizers for a Multi-Marginal Optimal Transport Problem with Intermolecular Interactions Cost
    (2024) Gerolin, Augusto; Petrache, Mircea; Vargas-Jimenez, Adolfo
    We investigate a new multi -marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we introduce such dissociation model, the corresponding optimal transport problem as well as show preliminary results on the existence and uniqueness of Monge solutions assuming absolute continuity of at least two of the marginals. Finally, we show that such marginal regularity conditions are necessary for the existence of an unique Monge solution.
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    Optimal and non-optimal lattices for non-completely monotone interaction potentials
    (2019) Betermin, Laurent; Petrache, Mircea
    We investigate the minimization of the energy per point Ef among d-dimensional Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric function f(|x|2). We formulate criteria for minimality and non-minimality of some lattices for Ef at fixed scale based on the sign of the inverse Laplace transform of f when f is a superposition of exponentials, beyond the class of completely monotone functions. We also construct a family of non-completely monotone functions having the triangular lattice as the unique minimizer of Ef at any scale. For Lennard-Jones type potentials, we reduce the minimization problem among all Bravais lattices to a minimization over the smaller space of unit-density lattices and we establish a link to the maximum kissing problem. New numerical evidence for the optimality of particular lattices for all the exponents are also given. We finally design one-well potentials f such that the square lattice has lower energy Ef than the triangular one. Many open questions are also presented.
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    Steady State Kinetics for Enzymes with Multiple Binding Sites Upstream of the Catalytic Site
    (2023) Osorio, Manuel I.; Petrache, Mircea; Salinas, Dino G.; Valenzuela-Ibaceta, Felipe; Gonzalez-Nilo, Fernando; Tiznado, William; Perez-Donoso, Jose M.; Bravo, Denisse; Yanez, Osvaldo
    The Michaelis-Menten mechanism, which describes the binding of a substrate to an enzyme, is a simplification of the process on a molecular scale. A more detailed model should include the binding of the substrate to precatalytic binding sites (PCBSs) prior to the transition to the catalytic site. Our work shows that the incorporation of PCBSs, in steady-state conditions, generates a Michaelis-Menten-type expression, in which the kinetic parameters KM and Vmax adopt more complex expressions than in the model without PCBSs. The equations governing reaction kinetics can be seen as generalized symmetries, relative to time translation actions over the state space of the underlying chemical system. The study of their structure and defining parameters can be interpreted as looking for invariants associated with these time evolution actions. The expression of KM decreases as the number of PCBSs increases, while Vmax reaches a minimum when the first PCBSs are incorporated into the model. To evaluate the trend of the dynamic behavior of the system, numerical simulations were performed based on schemes with different numbers of PCBSs and six conditions of kinetic constants. From these simulations, with equal kinetic constants for the formation of the Substrate/PCBS complex, it is observed that KM and Vmax are lower than those obtained with the Michaelis-Menten model. For the model with PCBSs, the Vmax reaches a minimum at one PCBS and that value is maintained for all of the systems evaluated. Since KM decreases with the number of PCBSs, the catalytic efficiency increases for enzymes fitting this model. All of these observations are consistent with the general equation obtained. This study allows us to explain, on the basis of the PCBS to KM and Vmax ratios, the effect on enzyme parameters due to mutations far from the catalytic site, at sites involved in the first enzyme/substrate interaction. In addition, it incorporates a new mechanism of enzyme activity regulation that could be fundamental to search for new activity-modulating sites or for the design of mutants with modified enzyme parameters.
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