Journal of American Association for Pediatric Ophthalmology and Strabismus

(1980). Electric, Optic and Acoustic Interactions in Dielectrics. Optica Acta: International Journal of Optics: Vol. 27, No. 6, pp. 732-733.

Electric, Optic and Acoustic Interactions in Dielectrics

Fractal neutrons diffusion equation: Uniformization of heat and fuel burn-up in nuclear reactor

A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed. On the basis of the theory, the Schrodinger equation and the energy spectrum for the quantum LC circuit were derived. By introducing special forms of position-dependent LC-electric components, the associated creation and annihilation operators were obtained and analyzed. The quantization of the DC-driven Josephson circuit and its parametric amplifier were studied in details. The main outcome of this study concerns the finite form of the energy expectation value at very high temperature in contrast to the results obtained in literature which is time-dependent. Further details were analyzed and discussed.

Quantization of Foster mesoscopic circuit and DC-pumped Josephson parametric amplifier from fractal measure arguments

In this study, we have constructed a generalized Schrodinger equation in fractal dimensions characterized by an effective potential which is generated by a position-dependent mass. Our analysis is based on the fractal anisotropy and product-like fractal measure approach introduced by Li and Ostoja-Starzewski in their formulation of continuum media. Our analysis is based on the von Roos phenomenological approach and is characterized by a parametric ordering ambiguity $${{\varvec{\upalpha}}},{{\varvec{\upbeta}}},{{\varvec{\upgamma}}}$$
 which arises in the Schrodinger Hamiltonian as a result of the non-unique representation of the kinetic energy term. We have selected numerical values of von Roos parameters different from the trivial case, and we have solved the corresponding generalized Schrodinger equation for different forms of the position-dependent mass. This study was proved to be practical to analyze several effective physical properties of nanostructures including quantum dots and quantum box that are relevant to overall photonics and exciton spectroscopy in quantum-well structures.

Quantum dots and cuboid quantum wells in fractal dimensions with position-dependent masses

Entropy dynamics is a Bayesian inference methodology that quantifies posterior probability densities and associated phases as a sequence of snap-shots in time to estimate the most likely material particle positions as a function of external stimuli (e.g., heat, traction, electromagnetic fields, chemicals, etc.). The inference method provides a means to create models at the continuum and quantum scales purely based on probability inference. Here we explore its application to fractal structure and fractional properties for polymer mechanics. We investigate how fractal polymer network structure influences the hyper-elastic constitutive behavior for a broad class of polymers such as auxetic foams, dielectric elastomers, and liquid crystal elastomers which can exhibit fractal structure and have applications in the development of adaptive structures.

Entropy dynamics approach to fractional order mechanics with applications to elastomers

Smooth orthogonal projections with good localization properties were originally studied in the wavelet literature as a way to both understand and generalize the construction of smooth wavelet bases on $L^{2}(\mathbb {R})$. Smoothness plays a critical role in the construction of wavelet bases and their generalizations as it is instrumental to achieve excellent approximation properties. In this paper, we extend the construction of smooth orthogonal projections to higher dimensions, a challenging problem in general for which relatively few results are found in the literature. Our investigation is motivated by the study of multidimensional nonseparable multiscale systems such as shearlets. Using our new class of smooth orthogonal projections, we construct new smooth Parseval frames of shearlets in $L^{2}(\mathbb {R}^{2})$ and $L^{2}(\mathbb {R}^{3})$.

Smooth projections and the construction of smooth Parseval frames of shearlets

Fractional and fractal order effects in soft elastomers: Strain rate and temperature dependent nonlinear mechanics

Recently we employed entropy dynamics, a statistical inference tool that facilitates quantifying posterior probabilities of likely particle positions, to create material models relating fractal polymers networks to their constitutive behaviors.1 This methodology is applicable to classical mechanics, electromagnetic field theory, and quantum mechanics, thus offering new opportunities to expand our understating of functional materials. The entropy dynamics approach usually starts by maximizing Shannon entropy of possible particle locations with added constraints to account for particle interactions or motion. Here, we take a broader approach and use the Renyi entropy, a generalization of the Shannon entropy, to build our constitutive models for multi-functional polymers. The Renyi entropy allows us to derive wide-ranging material constitutive models that consolidate other entropy approaches such as max-entropy, min-entropy, and collision entropy. Furthermore, we investigate material properties using fractional moment constraints instead of the widely used integer moment constraints. Finally, we show how our approach provides a way to building models relevant to a broad class of smart materials and structures.

Basanta R. Pahari

Papers

Entropy dynamics approach to fractional order mechanics with applications to elastomers

Smooth projections and the construction of smooth Parseval frames of shearlets

Fractional and fractal order effects in soft elastomers: Strain rate and temperature dependent nonlinear mechanics

Renyi entropy and fractional order mechanics for predicting complex mechanics of materials

Numerical simulation of the formation of spherulites in polycrystalline binary mixtures