Jovo P. Jarić

Fractional derivatives embody essential features of cell rheological behavior.

AbstractMechanical moduli of cultured airway smooth muscle cells (Fabry, B., et al. Phys. Rev. Lett. 87:148102, 2001) reveal that the frequency dependence of cell rheological behavior conforms to a weak power-law relationship over a wide range of frequency (10-2 -103 Hz).Such a behavior cannot be accounted for by standard viscoelastic models characterized by a discrete number of time constants that have been commonly used in previous studies of cell viscoelasticity. Fractional calculus, by contrast, provides a natural framework for describing weak power-law relationships and requires no assumptions about the type of material, the time constant distribution or the time/frequency interval in which rheological observations are made. In this study, we developed a rheological model of the cell using methods of fractional calculus. We used a least-squares technique to fit the model to data previously obtained from measurements on airway smooth muscle cells. The fit provided an excellent correspondence to the data, and the estimated values of model parameters were physically plausible. The model leads to a novel and unexpected empirical link between dynamic viscoelastic behavior of the cytoskeleton and the static contractile stress that it bears.

Size-dependent energy in crystal plasticity and continuum dislocation models.

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two questions relevant for the development of a mesoscale, size-dependent plasticity: (i) can the phenomenological expression for size-dependent energy, as quadratic form of Nyes dislocation density tensor, be justified from the point of view of dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physical expressions is possible, but only if the multiplicity of characteristic lengths associated with different slip systems, is sacrificed. Finally, we discuss the consequences of the assumption that a single length scale governs the plasticity of a crystal, and note that the plastic dissipation at interfaces has a strong dependence on the length scale embedded in the energy expression.

The energy release rate in quasi-static crack propagation and J-integral

Abstract The energy release rate and its relation with J-integral is considered from some general point of view.

On the Representation of Symmetric Isotropic 4-Tensors

This note provides short proof of the representation of a symmetric isotropic 4-tensor in an n-dimensional real Euclidean space.

FOURIER'S LAW OF HEAT CONDUCTION IN A NONLINEAR FLUID

The problem of deriving Fouriers law of heat conduction in a nonlinear fluid is considered. As a basis for its derivation, Mullers entropy principle and the assumption introduced by I-Shih Liu are used. It is shown that the absolute temperature, derived in this way, is the same for both linear and nonlinear fluids. Contrary to the absolute temperature, we show that the functional form of the heat flux vector, which characterizes Fouriers law of heat conduction, depends on the first gradient theory of heat conducting fluid.

On the gradients of the principal invariants of a second-order tensor

In this paper the gradients of the principal invariants of an arbitrary second-order tensor are derived in a very concise way.

On the inverse Noether's theorem in nonlinear micropolar continua

In this article, the modified Noethers theorem is established in general form. Then, the inverse theorem is used in nonlinear micropolar continua in order to derive one-parameter family of transformations under which the corresponding functional is invariant. Next, the conservation laws are written. They include, as a special case, the conservation laws of micropolar elastostatics, the balance laws of elastodynamics and elastostatics. We do not analyse any of these special cases, because they may be obtained very easily.

THERMODYNAMICS OF NON-SIMPLE HEAT-CONDUCTING INTERFACE

Abstract Following Moeckels approach, thermodynamics of non-simple, heat-conducting material interface is investigated. In order to obtain field equations for the fields of mass density, motion, and temperature in the interface, specific balance equations are used for mass, momentum, moment of momentum, and energy in the surface, and constitutive equations are stated. The constitutive equations of the bulk material (the three-dimensional non-simple, heat-conducting fluid) were derived by I-Shih Liu. The forms of all of these constitutive equations are restricted by an entropy principle which is adopted from Mullers entropy principle.