scispace - formally typeset
Search or ask a question
Author

Massiliano Zingales

Bio: Massiliano Zingales is an academic researcher. The author has contributed to research in topics: State variable & Fractional calculus. The author has an hindex of 1, co-authored 1 publications receiving 27 citations.

Papers
More filters
Journal ArticleDOI
TL;DR: In this article, the authors considered the condition that different histories delivering the same response are such that the fractional derivative of their difference is zero for all times, and provided an approximation formula for the residual stress associated to the difference of the histories above.
Abstract: The widespread interest on the hereditary behavior of biological and bioinspired materials motivates deeper studies on their macroscopic ``minimal" state. The resulting integral equations for the detected relaxation and creep power-laws, of exponent $\beta$, are characterized by fractional operators. Here strains in $SBV_{loc}$ are considered to account for time-like jumps. Consistently, starting from stresses in $L_{loc}^{r}$, $r\in [1,\beta^{-1}], \, \, \beta\in(0,1)$ we reconstruct the corresponding strain by extending a result in [42]. The ``minimal" state is explored by showing that different histories delivering the same response are such that the fractional derivative of their difference is zero for all times. This equation is solved through a one-parameter family of strains whose related stresses converge to the response characterizing the original problem. This provides an approximation formula for the state variable, namely the residual stress associated to the difference of the histories above. Very little is known about the microstructural origins of the detected power-laws. Recent rheological models, based on a top-plate adhering and moving on functionally graded microstructures, allow for showing that the resultant of the underlying ``microstresses" matches the action recorded at the top-plate of such models, yielding a relationship between the macroscopic state and the ``microstresses".

27 citations


Cited by
More filters
Journal ArticleDOI
TL;DR: Fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials.
Abstract: Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can ...

64 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduce real analysis for real analysis in the context of real data analysis, and propose a real analysis framework for real data collection and analysis, using real data.
Abstract: Introductory real analysis , Introductory real analysis , کتابخانه دیجیتال جندی شاپور اهواز

49 citations

Journal ArticleDOI
TL;DR: Theoretical results show that differences in stiffness allow healthy and cancer cells to be discriminated, by highlighting frequencies associated with resonance-like phenomena—prevailing on thermal fluctuations—that could be helpful in targeting and selectively attacking tumour cells.
Abstract: Experimental studies recently performed on single cancer and healthy cells have demonstrated that the former are about 70% softer than the latter, regardless of the cell lines and the measurement technique used for determining the mechanical properties. At least in principle, the difference in cell stiffness might thus be exploited to create mechanical-based targeting strategies for discriminating neoplastic transformations within human cell populations and for designing innovative complementary tools to cell-specific molecular tumour markers, leading to possible applications in the diagnosis and treatment of cancer diseases. With the aim of characterizing and gaining insight into the overall frequency response of single-cell systems to mechanical stimuli (typically low-intensity therapeutic ultrasound), a generalized viscoelastic paradigm, combining classical and spring-pot-based models, is introduced for modelling this problem by neglecting the cascade of mechanobiological events involving the cell nucleus, cytoskeleton, elastic membrane and cytosol. Theoretical results show that differences in stiffness, experimentally observed ex vivo and in vitro, allow healthy and cancer cells to be discriminated, by highlighting frequencies (from tens to hundreds of kilohertz) associated with resonance-like phenomena—prevailing on thermal fluctuations—that could be helpful in targeting and selectively attacking tumour cells.

46 citations

Journal ArticleDOI
TL;DR: In this paper, the non-uniqueness of the free energy function is removed for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.

34 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the modeling of heat conduction by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order.
Abstract: The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo–Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo–Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo–Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier’s law does not.

29 citations