Germain Hubert Ben-Bolie

Energy transport in the three coupled α-polypeptide chains of collagen molecule with long-range interactions effect

The dynamics of three coupled α-polypeptide chains of a collagen molecule is investigated with the influence of power-law long-range exciton-exciton interactions. The continuum limit of the discrete equations reveal that the collagen dynamics is governed by a set of three coupled nonlinear Schrödinger equations, whose dispersive coefficient depends on the LRI parameter r. We construct the analytic symmetric and asymmetric (antisymmetric) soliton solutions, which match with the structural features of collagen related with the acupuncture channels. These solutions are used as initial conditions for the numerical simulations of the discrete equations, which reveal a coherent transport of energy in the molecule for r > 3. The results also indicate that the width of the solitons is a decreasing function of r, which help to stabilize the solitons propagating in the molecule. To confirm further the efficiency of energy transport in the molecule, the modulational instability of the system is performed and the numerical simulations show that the energy can flow from one polypeptide chain to another in the form of nonlinear waves.

Localized modulated wave solutions in diffusive glucose–insulin systems

Abstract We investigate intercellular insulin dynamics in an array of diffusively coupled pancreatic islet β -cells. The cells are connected via gap junction coupling, where nearest neighbor interactions are included. Through the multiple scale expansion in the semi-discrete approximation, we show that the insulin dynamics can be governed by the complex Ginzburg–Landau equation. The localized solutions of this equation are reported. The results suggest from the biophysical point of view that the insulin propagates in pancreatic islet β -cells using both temporal and spatial dimensions in the form of localized modulated waves.

Discrete energy transport in collagen molecules

The modulational instability in the three coupled α-polypeptide chains of a collagen molecule is investigated. Choosing symmetric and asymmetric solutions, and applying the so-called rotating-wave approximation, we describe the dynamics of the system by the discrete nonlinear Schrodinger (DNLS) equation. The linear stability analysis of the continuous wave solution is performed. The numerical simulations show the generation of trains of solitonic structures in the lattice with increasing amplitude as time progresses. The effect of damping and noise forces of the physiological temperature (T = 300 K) introduces an erratic behavior to the formed patterns, reinforcing the idea that the energy used in metabolic processes is confined to specific regions for efficiency.

MODULATIONAL INSTABILITY OF A BOSE–EINSTEIN CONDENSATE BEYOND THE FERMI PSEUDOPOTENTIAL WITH A TIME-DEPENDENT COMPLEX POTENTIAL

The modulational instability (MI) of Bose–Einstein condensates based on a modified Gross–Pitaevskii equation (GPE) which takes into account quantum fluctuations and a shape-dependent term, trapped in an external time-dependent complex potential is investigated. The external potential consists of an expulsive parabolic background with a complex potential and a gravitational field. The theoretical analysis uses a modified lens-type transformation which converts the modified GPE into a modified form without an explicit spatial dependence. A MI criterion and a growth rate are explicitly derived, both taking into account quantum fluctuations and the parameter related to the feeding or loss of atoms in the condensate which significantly affect the gain of instability of the condensate. Direct numerical simulations of the modified GPE show convincing agreements with analytical predictions. In addition, our numerical results also reveal that the gravitational field has three effects on the MI: (i) the deviation backward or forward of solitons trains, (ii) the enhancement of the appearance of the MI and (iii) the reduction of the lifetime of pulses. Moreover, numerical simulations proved that it is possible to control the propagation of the generated solitons trains by a proper choice of parameters characterizing both the loss or feeding of atoms and the gravitational field, respectively.

Solitary waves in an inhomogeneous chain of α-helical proteins

The dynamics of Davydovs model of α-helical proteins is considered by including the influence of inhomogeneities in the monomer units. Using the D2 ansatz for the exciton–phonon quantum state, the model Hamiltonian is transformed into a pair of classical lattice equations, which is further reduced in the continuum limit to a sole perturbed nonlinear Schrodinger (NLS) equation. The results of the perturbation theory of this equation show that the inhomogeneities in the localized form do not affect the velocity and amplitude of the solitary waves during propagation. We employ also the sine–cosine functions method to construct the exact solitary wave solutions in the presence of a variety of nonlinear inhomogeneities such as biquadratic, exponential and periodic inhomogeneities and it reveals that the coherent energy transport in the α-helical proteins is very much influenced by these nonlinear inhomogeneities.

Generation of Bright Matter-Wave Soliton Patterns in Mixtures of Bose-Einstein Condensates with Cubic and Quintic Nonlinearities

The modulational instability (MI) of binary condensates with cubic-quintic nonlinearities is investigated. Using a linear stability analysis, a gain of instability is derived then, effects of the quintic nonlinearities on the instability gain are identified. To be precise, attractive intraspecie quintic nonlinearities enhance the instability, while repulsive quintic intraspecie nonlinearities soften the instability. Besides, small attractive and large repulsive quintic inter-species nonlinearities increase the instability. Numerical experiments quite well corroborate the analytical predictions. Further numerical results show effects of the cubic and the quintic nonlinearities on the propagation of trains of bright solitons generated.

Stability of binary condensates with spatial modulations of quintic nonlinearities in optical lattices

The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.

THREE-BODY INTERACTIONS BEYOND THE GROSS PITAEVSKII EQUATION AND MODULATIONAL INSTABILITY OF BOSE EINSTEIN CONDENSATES

Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.

Variational approach for two-component condensates dynamics with two- and three-body interactions and external feeding

We study theoretically and numerically the dynamical behavior of two-component condensates with two- and three-body interactions in variable shape optical lattices and external feeding. By means of the variational approach, the evolution of the condensate amplitudes, widths and number of particles are investigated. The stability of stationary two-component solitons are derived through the Vakhitov–Kolokolov criterion which depends on the cubic and quintic nonlinearities. Direct numerical results of the two coupled Gross–Piteavskii equations (GPEs) which describe the dynamics of the two-component condensates are found to be in good agreement with the analytical predictions.