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1

Symplectic and time reversible integrator for rigid bodies

Kamberaj H., Low R.J., Neal M.P.

Systems Science

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2003

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Vol. 29, nr 2

31-45

EN

A symplectic and time-reversible molecular dynamics algorithm is presented for rigid molecules in the quaternion representation. The algorithm is developed on the basis of the Trotter factorisation scheme using a Hamiltonian formalism The structure is similar to that of the velocity Verlet algorithm. Subsequently we describe the coupling of the rigid bodies to a thermostat. The isothermal molecular dynamics is defined by introducing additional pseudo-friction coefficients, according to a generalised Nose-Hoover prescription.

2

New algorithms for solving the tasks scheduling problems in discrete manufacturing systems

Józefczyk J.

Systems Science

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2003

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Vol. 29, nr 4

85-98

EN

The new algorithms for solving the tasks scheduling problem with moving executors to minimize the sum of completion times are considered. The corresponding combinatorial optimization problem is formulated on the basis of the formulations of the problems for the other scheduling performance indices. The heuristic simulation annealing solution algorithm is presented. It is compared with the evolutionary solution algorithm using computer simulation experiments. The influence of the parameters of the solution algorithm as well as the tasks scheduling problem on the quality of results and on the time of computation is investigated.

3

Allosteric systems on biological membrane analysis by time minimum optimal control principle

Hirayama H., Okita Y.

Systems Science

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2000

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Vol. 26, nr 4

121-145

EN

We calculated temporal changes in concentrations of species in biological allosteric system. The allosteric nature was described by co-operativity and concerted actions of identical subunits composing the system. The co-operativity was characterized by accelerated bindings of substrates to the subunits and their structural changes. The concerted mechanism provokes all or non-conformational change of an entire molecule from its inactive to active sate at one time. As the number of bound substrate increases, the concerted conformational transition of all the subunits strongly directs to active state. These two properties save the time to complete activation of the system and full substrate binding. The allosteric actions are frequently observed in the critical emergency conditions such as oxygen binding, immune defense reaction and ionic channel gating on excitable membrane of the bio-signal transmission. Hence, the temporal actions of allosteric systems can be interpreted as the shortest time controlled system. We thus, proposed the time minimum optimal control principle as an organizing strategy for activating and binding processes of the allosteric systems. We presented fifteen non-linear differential equations for describing the temporal changes in concentrations of the species composing a two activators-two substrates allosteric system. Another set of fifteen non-linear differential equations for co-state variables were obtained by partial differentiation of the Hamiltonian of the system based on the minimum optimal control theory. The computed temporal concentrations of species oscillated. A reduction of an allosteric parameter shifted these temporal changes synchronously. When the amounts of substrate and activator were set as time invariant, the oscillations disappeared and the concentration of the species approached a steady level. These computed results are qualitatively consistent with actual biophysical phenomena. The present mathematical description of transient changes in concentrations of species in biological allosteric system will be available for evaluating the effective and economical performance of the allosteric system acting under the critical emergency circumstances.