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The various mathematical models developed in the past to interpret the behavior of natural and manmade materials were based on observations and experiments made at that time. Classical laws (such as Newton's for gravity, Hooke's for elasticity, Navier-Stokes for fluidity, Fick's/Fourier's for diffusion/heat transfer, Coulomb's for electricity, as well as Maxwell's for electromagnetism and Einstein's for relativity) formed the basis of current technology and shaping of our civilization. The discovery of new phenomena with the aid of recently developed experimental probes have led to various modifications of these laws across disciplines and the scale spectrum: from subatomic and elementary particle physics to cosmology and from atomistic and nano/micro to macro/giga scales. The emergence of nanotechnology and the further advancement of space technology are ultimately connected with the design of novel tools for observation and measurements, as well as the development of new methods and approaches for quantification and understanding. The paper first reviews the author's previously developed weakly nonlocal or gradient models for elasticity, diffusion and plasticity within a unifying internal length gradient (ILG) framework. It then proposes a similar extension for fluids and Maxwell's equations of electromagnetism. Finally, it ventures a gradient modification of Newton's law of gravity and examines its implications to some problems of elementary particle physics, also relevant to cosmology. Along similar lines, it suggests an analogous extension of London's quantum mechanical potential to include both an "attractive" and a "repulsive" branch. It concludes with some comments on a fractional generalization of the ILG framework.

Motivated by the endeavors of Li Xiang and You-Gen Shen on naked singularities, we investigate the validity of the cosmic censorship conjecture in the context of generalized uncertainty principle. In particular, upon considering both linear and quadratic terms of momentum in the uncertainty principle, we first compute the entropy of a massless charged black hole in de Sitter spacetime at a given modified temperature. Then, we compute the corresponding modified cosmological radius and express the black hole electric charge in terms of this modified cosmological radius and, thus, in terms of the generalized uncertainty principle parameter. Finally, we examine whether such a system will end up being a naked singularity or it might be protected by the cosmic censorship conjecture, and how that might be related to the possible existence of massless charged particles., Comment: v1: 8 pages, 4 figures, RevTex

Motivated by the works on Equivalence Principle in the context of linear Generalized Uncertainty Principle and, independently, in the context of quadratic Generalized Uncertainty Principle, we expand these endeavors in the context of Generalized Uncertainty Principle when both linear and quadratic terms in momentum are include. We demonstrate how the definitions of equations of motion change upon that expansion. We also show how to obtain an analogue of Liouville theorem in the presence of linear and quadratic Generalized Uncertainty Principle. We employ the corresponding modified invariant unit volume of phase space to discuss the resulting density of states, the problem of cosmological constant, the black body radiation in curved spacetime, the concurrent energy and consequent no Brick Wall entropy., Comment: v1: 10 pages, RevTex, 7 figures; v2: references updated, one footnote added; v3: two footnotes and references added, no change in physics, to appear in EPJC

Motivated by a recent work by Yongwan Gim, Hwajin Um, and Wontae Kim, we investigate the validity of the no-cloning theorem in the context of generalized uncertainty principle. In particular, in the presence of linear and quadratic terms of momentum in generalized uncertainty principle, we first compute the energy density at a given modified temperature and then using the modified Stefan-Boltzmann law we derive the modified Page time. Finally, we calculate the modified required energy for the information to be encoded into a message and be sent to an observer inside the black hole., Comment: v1: 11 pages, 1 figure; v2: clarifications added, no change in physics, to appear in EPJC

In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We derive a generalization of three-dimensional continuum gradient elasticity theory, starting from integral relations and assuming a weak non-locality of power-law type that gives constitutive relations with fractional Laplacian terms, by utilizing the fractional Taylor series in wave-vector space. In the sequel we consider non-linear field equations with fractional derivatives of non-integer order to describe nonlinear elastic effects for gradient materials with power-law long-range interactions in the framework of weak non-locality approximation. The special constitutive relationship that we elaborate on, can form the basis for developing a fractional extension of deformation theory of gradient plasticity. Using the perturbation method, we obtain corrections to the constitutive relations of linear fractional gradient elasticity, when the perturbations are caused by weak deviations from linear elasticity or by fractional gradient non-locality. Finally we discuss fractal materials described by continuum models with non-integer dimensional spaces. Using the recently suggested vector calculus for non-integer dimensional spaces, we consider problems of fractal gradient elasticity., Comment: 37 pages, Submitted to Acta Mechanica 2018 (ISSN: 0001-5970)

In this work we compute the entropy density, speed of sound, and the resulting impact on the bulk viscosity to shear viscosity ratio of an ideal Quark Gluon Plasma when the effects of a generalized uncertainty principle are taken into consideration. When the parameter of the generalized uncertainty principle tends to zero, i.e., $\alpha \rightarrow 0$, we obtain the value of the speed of sound for the ideal gas of massless particles, i.e., $c^{2}_{s}\rightarrow 1/3$, and we recover the expected result that the bulk viscosity $\zeta \rightarrow 0$ when $\alpha \rightarrow 0$. In addition, in the high temperature limit, i.e., $T\rightarrow \infty$, the speed of sound satisfies the equation $c^{2}_{s}\rightarrow 1/4$. The consequence this has on the bulk viscosity is that in the high temperature limit, the ratio of the bulk to shear viscosity $\zeta/\eta \rightarrow 5/48$. Our results suggest that the GUP introduces a scale into the system breaking the a priori conformal invariance of a system of massless noninteracting particles., Comment: 7 pages, no figures, REVTeX 4, to appear in NPB

It is well-known that perturbative quantum gravity is non-renormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this essay, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitational Higgs mechanism using spin connection as a gauge field, and show that this provides a mechanism for the effective reduction in the dimensionality of spacetime., Comment: This essay received an honorable mention in the 2018 Gravity Research Foundation Essay Competition on Gravitation; v2: change of counting of d.o.f. from (3+1) to (d+1) spacetime dimensions, references updated

Advances in data collection and data storage technologies have given way to the establishment of transactional databases among companies and organizations, as they allow enormous amounts of data to be stored efficiently. Useful knowledge can be mined from these data, which can be used in several ways depending on the nature of the data. Quite often companies and organizations are willing to share data for the sake of mutual benefit. However, the sharing of such data comes with risks, as problems with privacy may arise. Sensitive data, along with sensitive knowledge inferred from this data, must be protected from unintentional exposure to unauthorized parties. One form of the inferred knowledge is frequent patterns mined in the form of frequent itemsets from transactional databases. The problem of protecting such patterns is known as the frequent itemset hiding problem. In this paper we present a toolbox, which provides several implementations of frequent itemset hiding algorithms. Firstly, we summarize the most important aspects of each algorithm. We then introduce the architecture of the toolbox and its novel features. Finally, we provide experimental results on real world datasets, demonstrating the efficiency of the toolbox and the convenience it offers in comparing different algorithms.

Motivated by a recent work of Scardigli, Lambiase and Vagenas (SLV), we derive the GUP parameter, i.e. $\alpha_0$, when the GUP has a linear and quadratic term in momentum. The value of the GUP parameter is obtained by conjecturing that the GUP-deformed black hole temperature of a Schwarzschild black hole and the modified Hawking temperature of a quantum-corrected Schwarzschild black hole are the same. The leading term in both cases is the standard Hawking temperature and since the corrections are considered as thermal, the modified and deformed expressions of temperature display a slight shift in the Hawking temperature. Finally, by equating the first correction terms, we obtain a value for the GUP parameter. In our analysis, the GUP parameter is not a pure number but depends on the ratio $\mpl /M$ with $\mpl$ to be the Planck mass and $M$ the black hole mass., Comment: v1: 10 pages, no figures, REVTeX 4; v2: typos corrected and references updated to match published version

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect., Comment: 8 pages, 2 figures, revtex4, to appear in EJP

Following a phenomenological analysis done by the late Martin Perl for the detection of the dark energy, we show that an axion of energy $1.5\times 10^{-3}~eV/c^2$ can be a viable candidate for the dark energy particle. In particular, we obtain the characteristic length and frequency of the axion as a quantum particle. Then, employing a relation that connects the energy density with the frequency of a particle, i.e., $\rho\sim f^{4}$, we show that the energy density of axions, with the aforesaid value of mass, as obtained from our theoretical analysis is proportional to the dark energy density computed on observational data, i.e., $\rho_{a}/\rho_{DE}\sim \mathcal{O}(1)$., Comment: 3 pages, REVTeX 4, no figures, to appear in Kuwait J.Sci

It is believed that classical behavior emerges in a quantum system due to decoherence. It has also been proposed that gravity can be a source of this decoherence. We examine this in detail by studying a number of quantum systems, including ultra-relativistic and non-relativistic particles, at low and high temperatures in an expanding Universe, and show that this proposal is valid for a large class of quantum systems., Comment: 7 pages, REVTeX 4, no figures, to appear in IJMPD

In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalized uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters $\beta_0$ and $ \alpha_0$ with $\eta$ which is the parameter that characterizes the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation parameter $\beta_0$. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime., Comment: V1: 5 pages, REVTeX 4, 4 figures; v2: 6 pages, version accepted in NPB; v3: references updated, to appear in NPB

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. Technically, the model pans out as a system of coupled {\it Fick type} diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two non-equilibrium local temperature baths e.g. ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, {\it i.e.}, by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified timescale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real life fluctuating environments., Comment: 17 pages, 9 figures; Physical Review E (accepted)