arXiv subjects

Valery B. Kokshenev

Publications and source records attributed to Valery B. Kokshenev.

10 recordsLinked to original sources

arXiv2009

Scaling functional patterns of skeletal and cardiac muscles: New non-linear elasticity approach

Responding mechanically to environmental requests, muscles show a surprisingly large variety of functions. The studies of in vivo cycling muscles qualified skeletal muscles into four principal locomotor patterns: motor, brake, strut, and spring. While much effort of has been done in searching for muscle design patterns, no fundamental concepts underlying empirically established patterns were revealed. In this interdisciplinary study, continuum mechanics is applied to the problem of muscle structure in relation to function. The ability of a powering muscle, treated as a homogenous solid organ, tuned to efficient locomotion via the natural frequency is illuminated through the non-linear elastic muscle moduli controlled by contraction velocity. The exploration of the elastic force patterns known in solid state physics incorporated in activated skeletal and cardiac muscles via the mechanical similarity principle yields analytical rationalization for locomotor muscle patterns. Besides the explanation of the origin of muscle allometric exponents observed for muscles in legs of running animals and wings of flying birds, the striated muscles are patterned through primary and secondary activities expected to be useful in designing of artificial muscles and modeling living and extinct animals.

physics.bio-ph↗

arXiv2009

Salient features in locomotor evolutionary adaptations of proboscideans revealed via the differential scaling of limb long bones

The standard differential scaling of proportions in limb long bones (length against circumference) is applied to a phylogenetically wide sample of the Proboscidea, Elephantidae and the Asian (Elephas maximus) and African elephant (Loxodonta africana). In order to investigate allometric patterns in proboscideans and terrestrial mammals with parasagittal limb kinematics, the computed slopes (slenderness exponents) are compared with published values for mammals and studied within a framework of theoretical models of long bone scaling under gravity and muscle forces. Limb bone allometry in E. maximus and the Elephantidae are congruent with adaptation to bending and/or torsion induced by muscular forces during fast locomotion, as in other mammals, whereas limb bones in L. africana appear adapted for coping with the compressive forces of gravity. Consequently, hindlimb bones are expected to be more compliant than forelimb bones in accordance with in vivo studies on elephant locomotory kinetics and kinematics, and the resultant negative limb compliance gradient in extinct and extant elephants, which contrasts to other mammals, suggests an important locomotory constraint preventing achievement of a full-body aerial phase during locomotion. Differences in ecology may be responsible for the subtle differences observed between African and Asian elephant locomotion, and the more pronounced differences in allometric and mechanical patterns established in this study. Key words: long bone scaling models; standard differential scaling; limb gradient functions; proboscideans; extinct and extant elephants

physics.bio-ph↗

arXiv2009

Key principle of the efficient running, swimming, and flying

Empirical observations indicate striking similarities among locomotion in terrestrial animals, birds, and fish, but unifying physical grounds are lacking. When applied to efficient locomotion, the analytical mechanics principle of minimum action yields two patterns of mechanical similarity via two explicit spatiotemporal coherent states. In steady locomotory modes, the slow muscles determining maximal optimum speeds maintain universal intrinsic muscular pressure. Otherwise, maximal speeds are due to constant mass-dependent stiffness of fast muscles generating a uniform force field, exceeding gravitation. Being coherent in displacements, velocities and forces, the body appendages of animals are tuned to natural propagation frequency through the state-dependent elastic muscle moduli. Key words: variational principle of minimum action (04.20.Fy), locomotion (87.19.ru), biomechanics (87.85.G-).

physics.bio-ph↗

arXiv2009

To the problem of cross-bridge tension in steady muscle shortening and lengthening

Despite the great success of the Huxley sliding filament model proposed half a century ago for actin-myosin linkages (cross-bridges), it fails to explain the force-velocity behavior of stretching skeletal muscles. Huxley's two-state kinetic equation for cross-bridge proportions is therefore reconsidered and a new solution to the problem of steady muscle eccentric and concentric contractions is reported. When the second law of statistical thermodynamics is applied to cross-bridge proportions, the weakly bound states appear to be correlated to the strongly bound states via structural and kinetic intrinsic muscle characteristics. The explicit force-velocity curve fits the empirical tension-velocity data on frog muscle shortening using only one adjustable parameter, while the Huxley model employed four parameters.

physics.bio-ph↗

arXiv2005

On Chaotic Dynamics in Rational Polygonal Billiards

We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular motion in polygons is taken within the alternative deterministic and stochastic frameworks. The analysis is developed in terms of the billiard-wall collision distribution and the particle survival probability, simulated in closed and weakly open polygons, respectively. In the multi-vertex polygons, the late-time wall-collision events result in the circular-like regular periodic trajectories (sliding orbits), which, in the open billiard case are likely transformed into the surviving collective excitations (vortices). Having no topological analogy with the regular orbits in the geometrically corresponding circular billiard, sliding orbits and vortices are well distinguished in the weakly open polygons via the universal and non-universal relaxation dynamics.

math-ph↗

arXiv2004

Insights into the superdiffusive dynamics through collision statistics in periodic Lorentz gas and Sinai billiard

We report on the stationary dynamics in classical Sinai billiard (SB) corresponding to the unit cell of the periodic Lorentz gas (LG) formed by square lattice of length $L$ and dispersing circles of radius $R$ placed in the center of unit cell. Dynamic correlation effects for classical particles, initially distributed by random way, are considered within the scope of deterministic and stochastic descriptions. A temporal analysis of elastic reflections from the SB square walls and circle obstacles is given for distinct geometries in terms of the wall-collision and the circle-collision distributions. Late-time steady dynamic regimes are explicit in the diffusion exponent $z(R)$, which plays a role of the order-disorder crossover dynamical parameter. The ballistic ($z_{0}=1$) ordered motion in the square lattice (R=0) switches to the superdiffusion regime with $z_{1}=1.5$, which is geometry-independent when $R<L\sqrt{2}/4$. This observed universal dynamics is shown to arise from long-distance particle jumps along the diagonal and nondiagonal Bleher corridors in the LG with the infinite horizon geometry. In the corresponding SB, this universal regime is caused by the long-time wall-collision memory effects attributed to the bouncing-ball orbits. The crossover nonuniversal behavior with $1.5<z<2$ is due to geometry with $L\sqrt{2}/4\leq R<L/2$, when only the nondiagonal corridors remain open. All the free-motion corridors are closed in LG with finite horizon ($R\geq L/2$) and the interplay between square and circle geometries results in the chaotic dynamics ensured by the normal Brownian diffusion ($z_{2}=2$) and by the normal Gaussian distribution of collisions.

math-ph↗

arXiv2004

Dynamics of Human Walking

The problem of biped locomotion at steady speeds is discussed through a Lagrangian formulation developed for velocity-dependent, body driving forces. Human walking on a level surface is analyzed in terms of the data on the resultant ground-reaction force and the external work. It is shown that the trajectory of the center of mass is due to a superposition of its rectilinear motion with a given speed and a backward rotation along a shortened hypocycloid. A stiff-to-compliant crossover between walking gaits is described and the maximum speed for human walking, given by an instability of the trajectory, is predicted. Key words: locomotion, integrative biology, muscles, bipedalism, human walking, biomechanics.

physics.bio-ph↗

arXiv2002

Observation of Mammalian Similarity Through Allometric Scaling Laws

We discuss the problem of observation of natural similarity in skeletal evolution of terrestrial mammals. Analysis is given by means of testing of the power scaling laws established in long bone allometry, which describe development of bones (of length $L$ and diameter $D$) with body mass in terms of the growth exponents, \QTR{it}{e.g.} $λ=d\log L/d\log D$. The bone-size evolution scenario given three decades ago by McMahon was quiet explicit on the geometrical-shape and mechanical-force constraints that predicted $λ=2/3$. This remains too far from the mammalian allometric exponent $λ^{(\exp)}=0.80\pm 0.2$, recently revised by Christiansen, that is a chief puzzle in long bone allometry. We give therefore new insights into McMahon's constraints and report on the first observation of the critical-elastic-force, bending-deformation, muscle-induced mechanism that underlies the allometric law with estimated $λ=0.80\pm 0.3$. This mechanism governs the bone-size evolution with avoiding skeletal fracture caused by muscle-induced peak stresses and is expected to be unique for small and large mammals.

physics.bio-ph↗

arXiv2002

Description of the Primary Relaxation in Supercooled Liquids Through the Timescale Steepness Function

The primary relaxation in glass forming supercooled liquids (SCLs) above the glass transformation temperature T_g is discussed in terms of the first-order (steepness) and the second-order (curvature) temperature derivatives of the observed primary relaxation timescale. We report new insights into the problem of the domain of the Vogel-Fulcher-Tamman (VFT) equation, raised by Stickel et al. (J. Chem. Phys.,1995, 1996) and discussed by Richert and Angell (ibid., 1998). A new ergodic-cluster Gaussian statistical approach to the problem is given based on Onsager's thermodynamic principle. The primary relaxation is described by the VFT equation below the crossover temperature T_c (known from mode coupling theory (MCT)), and above T_c by an extended (VFTE) equation obtained after accounting for cluster-size fluctuations. The timescale is parametrized by a finite number of observable parameters such as the steepness function m_T, the MCT slowing-down exponent gamma_c, and the VFT and VFTE strength indices D_g and D_c. The latter are defined at T_g and T_c, respectively, for the strongly and moderately SCL states, which show absolute thermodynamic instability at the same VFT temperature T_0, associated with the Kauzmann temperature. For both states the limiting cluster-size characteristics are derived from experiment. A thermodynamic-dynamic correspondence is established between the dynamic VFT equation and the thermodynamic Adam and Gibbs model. The problem of the irregular SCLs, which are not consistent with the standard VFT equation, such as salol, ortho-terphenyl, and bis-methoxy-enyl-cyclohexane, is also discussed.

physics.chem-ph↗

arXiv2002

Slow relaxation in weakly open vertex-splitting rational polygons

The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two distinct channels for the late-time relaxation of type 1/t^delta are established. The primary channel, associated with the universal relaxation of ''regular'' orbits, with delta = 1, is common for both the closed and open, chaotic and nonchaotic billiards. The secondary relaxation channel, with delta > 1, is originated from ''irregular'' orbits and is due to the rationality of vertices.

physics.data-an↗