Edwards's statistical mechanics of crumpling networks in crushed self-avoiding sheets with finite bending rigidity

Statistical mechanics of cell aggregates: explaining the phase transition and paradoxical piezoelectric behavior of soft biological tissues

Piezoelectricity in biological soft tissues is a controversial issue with differing opinions. While there is compelling experimental evidence to suggest a piezoelectric-like response in tissues such as the aortic wall (among others), there are equally compelling experiments that argue against this notion. In addition, the lack of a polar structure in the underlying components of most soft biological tissues supports the latter. In this paper, we address the collective behavior of cells within a two-dimensional cell aggregate from the viewpoint of statistical mechanics. Our starting point is the simplest form of energy for cell behavior that only includes known observable facts e.g., the electrical Maxwell stress or electrostriction, resting potential across cell membranes, elasticity, and we explicitly exclude any possibility of electromechanical coupling reminiscent of piezoelectricity at the cellular level. We coarse-grain our cellular aggregate to obtain its emergent mechanical, physical, and electromechanical properties. Our findings indicate that the fluctuation of cellular strain (E) plays a similar role as the absolute temperature in a conventional atomistic-level statistical model. The coarse-grained effective free energy reveals several intriguing features of the collective behavior of cell aggregates, such as solid-fluid phase transitions and a distinct piezoelectric-like coupling, even though it is completely absent at the microscale. Closed-form formulas are obtained for key electromechanical properties, including stiffness, effective resting potential, critical E2-temperature (or fluctuation) for solid-fluid phase transitions, and apparent piezoelectric coupling in terms of fluctuation and electric potential regulated by active cellular processes.

Multifractal approach for a biological porous media: Human dentin case

A multifractal characterization to human dentin porosity is made. Micrographs of human dentin samples gotten from scanning electron microscopy (SEM) were studied in order to characterize porosity. We got the generalized dimensions (multifractal moments)D q for pore space and matrix skeleton on gray scale and binary images for samples of both gender. For the case, we found that superficial porosityη s is linked to mass fractal dimensionD 0 in an approximately linear relationship asD 0 ≈ η s + d ¯ for binary images. In addition, probability density distribution (PDD) for pore diameters is found a normal PDD type. Other quantities of interest like mean, standard deviation, maximum and minimum pore diameters, voit ratios, and percentage of chemical composition are reported. RESEARCH HIGHLIGHTS: SEM sample, images and procedure for multifractal analysis are detailed. Micro patterns in grayscale are multifractal and in binary scale are monofractals. Superficial porosity is relate to mass fractal dimension approximately linearly. From the porosity values, voit ratios are determined. Pores diameters obey a normal PDD.

A model for the fragmentation kinetics of crumpled thin sheets

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.

Effective degrees of freedom of a random walk on a fractal

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.