On a mathematical model of immune competition

Cattani, Carlo; Ciancio, Alexandre; Lods, Bertrand

doi:10.1016/j.aml.2005.09.001

Cited by 18 publications

(14 citation statements)

References 7 publications

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“…Future work will involve the following items for the application of the fractional calculus-based approach that is used in this paper within: (1) quantum and nano computing systems [52], (2) nanobeams, materials and medical applications [52][53][54], (3) fractal-based formulations to the microquasistatic thermoviscoelastic creep for rough surfaces in contact [55], and (4) other beam configurations for various types of nonlinearities, damping characteristics, and moving vehicles.…”

Section: Discussionmentioning

confidence: 99%

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

Alkhaldi

Abu-Alshaikh

Al‐Rabadi

2013

Advances in Mathematical Physics

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This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam. The beam is attached to multi single-degree-of-freedom (SDOF) fractionally-damped systems, and it is subjected to a vehicle moving with a constant velocity. The damping characteristics of the beam and SDOF systems are described in terms of fractional derivatives. Three coupled second-order fractional differential equations are produced and then they are solved by combining the Laplace transform with the decomposition method. The obtained numerical results show that the dynamic response decreases as (a) the number of absorbers attached to the beam increases and (b) the damping-ratios of used absorbers and beam increase. However, there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. Furthermore, the obtained results show very good agreements with special case studies that were published in the literature.

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Section: Discussionmentioning

confidence: 99%

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

Alkhaldi

Abu-Alshaikh

Al‐Rabadi

2013

Advances in Mathematical Physics

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“…In addition, Wavelet numerical method is another way to get the solution of the fractional PDEs. In fact, the wavelet transform theory has been widely used in numerical analysis such as PDEs-based image processing [15][16][17], option pricing model [18], integrodifferential operators [19][20][21][22][23], and other nonlinear PDEs [24][25][26][27][28]. The wavelet functions possess many excellent numerical properties, such as orthogonality, interpolation, smoothness, and compact support, which are helpful in improving numerical accuracy and efficiency.…”

Section: Introductionmentioning

confidence: 99%

Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation

Mei

Zhu

2013

Advances in Mathematical Physics

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Metzler et al. introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a Boltzmann thermal heat bath. In this paper, we present an interval Shannon wavelet numerical method for the FFPE. In this method, a new concept named “dynamic interval wavelet” is proposed to solve the problem that the numerical solution of the fractional PDE is usually sensitive to boundary conditions. Comparing with the traditional wavelet defined in the interval, the Newton interpolator is employed instead of the Lagrange interpolation operator, so, the extrapolation points in the interval wavelet can be chosen dynamically to restrict the boundary effect without increase of the calculation amount. In order to avoid unlimited increasing of the extrapolation points, both the error tolerance and the condition number are taken as indicators for the dynamic choice of the extrapolation points. Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA).

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“…It is clear that many different factors and methodologies [19][20][21] can contribute to enzymatic temperature adaptation and that no single factor can be invoked to explain adaptation in general. Although considerable progress has been made in theoretical and experimental studies of the protein folding and thermal stability, our knowledge is still limited for fully understanding this subject especially on mathematical modeling [22,23]. Therefore, further investigations of the protein folding and thermal stability mechanisms are crucial since it may provide relevant information on the evolutionary aspects involved and on the general mechanisms underlying protein stability.…”

Section: Introductionmentioning

confidence: 99%

Molecular Dynamics Simulation of Barnase: Contribution of Noncovalent Intramolecular Interaction to Thermostability

Chen

et al. 2013

Mathematical Problems in Engineering

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Bacillus amyloliquefaciensribonuclease Barnase (RNase Ba) is a 12 kD (kilodalton) small extracellular ribonuclease. It has broad application prospects in agriculture, clinical medicine, pharmaceutical, and so forth. In this work, the thermal stability of Barnase has been studied using molecular dynamics simulation at different temperatures. The present study focuses on the contribution of noncovalent intramolecular interaction to protein stability and how they affect the thermal stability of the enzyme. Profiles of root mean square deviation and root mean square fluctuation identify thermostable and thermosensitive regions of Barnase. Analyses of trajectories in terms of secondary structure content, intramolecular hydrogen bonds and salt bridge interactions indicate distinct differences in different temperature simulations. In the simulations, Four three-member salt bridge networks (Asp8-Arg110-Asp12, Arg83-Asp75-Arg87, Lys66-Asp93-Arg69, and Asp54-Lys27-Glu73) have been identified as critical salt bridges for thermostability which are maintained stably at higher temperature enhancing stability of three hydrophobic cores. The study may help enlighten our knowledge of protein structural properties, noncovalent interactions which can stabilize secondary peptide structures or promote folding, and also help understand their actions better. Such an understanding is required for designing efficient enzymes with characteristics for particular applications at desired working temperatures.

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On a mathematical model of immune competition

Cited by 18 publications

References 7 publications

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation

Molecular Dynamics Simulation of Barnase: Contribution of Noncovalent Intramolecular Interaction to Thermostability

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