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Bilgin, Bilgesu Arif

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PhD Student

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Bilgesu Arif

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Bilgin

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Bilgin, Bilgesu Arif

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2013 - 20186

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Researcher Of Publications: search.filters.isAuthorOfPublication.8058e5ad-d6ba-45a1-a184-6f886e976201

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Now showing 1 - 6 of 6
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    Existence of an attractor and determining modes for structurally damped nonlinear wave equations
    (Elsevier Science Bv, 2018) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655
    The paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for structurally damped semi-linear wave equation partial derivative(2)(t)u(x, t) - Delta u(x, t)+gamma(-Delta)(theta)partial derivative(t) u(x,t) + f(u) = g(x), theta is an element of(0, 1), x is an element of Omega, t > 0 under homogeneous Dirichlet's boundary condition in a bounded domain Omega subset of R-3. We proved that the asymptotic behavior as t -> infinity of solutions of this problem is completely determined by dynamics of the first N Fourier modes, when N is large enough. We also proved that the semigroup generated by this problem when theta is an element of(1/2, 1) possesses an exponential attractor. (C) 2017 Elsevier B.V. All rights reserved.
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    A fast algorithm for analysis of molecular communication in artificial synapse
    (IEEE-Inst Electrical Electronics Engineers Inc, 2017) N/A; Department of Electrical and Electronics Engineering; Bilgin, Bilgesu Arif; Akan, Özgür Barış; PhD Student; Faculty Member; Department of Electrical and Electronics Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 6647
    In this paper, we analyze molecular communications (MCs) in a proposed artificial synapse (AS), whose main difference from biological synapses (BSs) is that it is closed, i.e., transmitter molecules cannot diffuse out from AS. Such a setup has both advantages and disadvantages. Besides higher structural stability, being closed, AS never runs out of transmitters. Thus, MC in AS is disconnected from outer environment, which is very desirable for possible intra-body applications. On the other hand, clearance of transmitters from AS has to be achieved by transporter molecules on the presynaptic membrane of AS. Except from these differences, rest of AS content is taken to be similar to that of a glutamatergic BS. Furthermore, in place of commonly used Monte Carlo-based random walk experiments, we derive a deterministic algorithm that attacks for expected values of desired parameters such as evolution of receptor states. To assess validity of our algorithm, we compare its results with average results of an ensemble of Monte Carlo experiments, which shows near exact match. Moreover, our approach requires significantly less amount of computation compared with Monte Carlo approach, making it useful for parameter space exploration necessary for optimization in design of possible MC devices, including but not limited to AS. Results of our algorithm are presented in case of single quantal release only, and they support that MC in closed AS with elevated uptake has similar properties to that in BS. In particular, similar to glutamatergic BSs, the quantal size and the density of receptors are found to be main sources of synaptic plasticity. On the other hand, the proposed model of AS is found to have slower decaying transients of receptor states than BSs, especially desensitized ones, which is due to prolonged clearance of transmitters from AS.
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    Non-existence of global solutions to nonlinear wave equations with positive initial energy
    (Amer Inst Mathematical Sciences-Aims, 2018) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655
    We consider the Cauchy problem for nonlinear abstract wave equations in a Hilbert space. Our main goal is to show that this problem has solutions with arbitrary positive initial energy that blow up in a finite time. The main theorem is proved by employing a result on growth of solutions of abstract nonlinear wave equation and the concavity method. A number of examples of nonlinear wave equations are given. A result on blow up of solutions with arbitrary positive initial energy to the initial boundary value problem for the wave equation under nonlinear boundary conditions is also obtained.
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    Preventing blow up by convective terms in dissipative PDE’s
    (Springer Basel Ag, 2016) Zelik, Sergey; N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member 0000-0002-6282-4027; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655
    We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized Kuramoto-Sivashinsky equation and KdV type equations. The following common scenario is established: adding sufficiently strong (in comparison with the destabilizing nonlinearity) convective terms to equation prevents the solutions from blowing up in a finite time and makes the considered system globally well-posed and dissipative and for weak enough convective terms the finite time blow up may occur similar to the case, when the equation does not involve convective term. This kind of result has been previously known for the case of Burger's type equations and has been strongly based on maximum principle. In contrast to this, our results are based on the weighted energy estimates which do not require the maximum principle for the considered problem.
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    Diffusion-based model for synaptic molecular communication channel
    (IEEE-Inst Electrical Electronics Engineers Inc, 2017) N/A; N/A; N/A; Department of Electrical and Electronics Engineering; Khan, Tooba; Bilgin, Bilgesu Arif; Akan, Özgür Barış; PhD Student; PhD Student; Faculty Member; Department of Electrical and Electronics Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; N/A; 6647
    Computational methods have been extensively used to understand the underlying dynamics of molecular communication methods employed by nature. One very effective and popular approach is to utilize a Monte Carlo simulation. Although it is very reliable, this method can have a very high computational cost, which in some cases renders the simulation impractical. Therefore, in this paper, for the special case of an excitatory synaptic molecular communication channel, we present a novel mathematical model for the diffusion and binding of neurotransmitters that takes into account the effects of synaptic geometry in 3-D space and re-absorption of neurotransmitters by the transmitting neuron. Based on this model we develop a fast deterministic algorithm, which calculates expected value of the output of this channel, namely, the amplitude of excitatory postsynaptic potential (EPSP), for given synaptic parameters. We validate our algorithm by a Monte Carlo simulation, which shows total agreement between the results of the two methods. Finally, we utilize our model to quantify the effects of variation in synaptic parameters, such as position of release site, receptor density, size of postsynaptic density, diffusion coefficient, uptake probability, and number of neurotransmitters in a vesicle, on maximum number of bound receptors that directly affect the peak amplitude of EPSP.
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    Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations
    (Academic Press Inc Elsevier Science, 2013) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655
    We obtain sufficient conditions on initial functions for which the initial boundary value problem for second order quasilinear strongly damped wave equations blow up in a finite time. (C) 2013 Elsevier Inc. All rights reserved.