MULTI-DIMENSIONAL COSMOLOGY AND DSR–GUP

A multi-dimensional cosmology with FRW type metric having four-dimensional spacetime and d-dimensional Ricci-flat internal space is considered with a higher-dimensional cosmological constant. The classical cosmology in commutative and Doubly Special Relativity–Generalized Uncertainty Principle (DSR–GUP) contexts is studied and the corresponding exact solutions for negative and positive cosmological constants are obtained. In the positive cosmological constant case, it is shown that unlike the commutative as well as GUP cases, in DSR–GUP case both scale factors of internal and external spaces after accelerating phase will inevitably experience decelerating phase leading simultaneously to a big crunch. This demarcation from GUP originates from the difference between the GUP and DSR–GUP algebras. The important result is that unlike GUP which results in eternal acceleration, DSR–GUP at first generates acceleration but prevents the eternal acceleration at late-times and turns it into deceleration

Integrated Treatment of Saline Oily Wastewater Using Sono-Electrokinetic Process, Degradation Mechanism, and Toxicity Assessment

Integration of sonication (US) with electrokinetic (EK) oxidation was studied for the treatment of a saline oily wastewater, as well as the effect of operating parameters, including pH, voltage, electrode distance (ED), sonication power, and reaction time on COD removal. A COD removal of 98 % was observed for the sono-electrokinetic (SEK) process with an applied voltage of 2.5 V, US power of 300 W, initial COD concentration of 3850 mg L–1, and reaction time of 9 h. The efficiency of SEK over sonication alone and EK oxidation alone was also confirmed with a higher pseudo-first-order reaction rate constant of 0.43 h–1, compared to values of 0.13 and 0.01 for alternative processes. In addition, the biodegradability of effluent was improved based on average oxidation state (AOS) and carbon oxidation state (COS) analysis. Oxygen consumption rate inhibition, dehydrogenase activity inhibition, and growth rate inhibition methods demonstrated the low toxicity of effluent (12–15 %) compared to influent. The current work indicated that SEK is a reliable and efficient technology for the treatment of saline oily wastewaters containing recalcitrant aromatic organics. This work is licensed under a Creative Commons Attribution 4.0 International License

Multi-Dimensional Cosmology and GUP

We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and $d$-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions.Comment: 21 pages, 15 figures, minor revision, references adde

Casimir effect in a two dimensional signature changing spacetime

We study the Casimir effect for free massless scalar fields propagating on a two-dimensional cylinder with a metric that admits a change of signature from Lorentzian to Euclidean. We obtain a nonzero pressure, on the hypersurfaces of signature change, which destabilizes the signature changing region and so alters the energy spectrum of scalar fields. The modified region and spectrum, themselves, back react on the pressure. Moreover, the central term of diffeomorphism algebra of corresponding infinite conserved charges changes correspondingly.Comment: 14 pages, abstract and text extended, references added, to appear in JM

Casimir effect for a spherical shell in de Sitter spacetime with signature change

The Casimir stress on a spherical shell in de Sitter signature changing background for massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different metric signatures and cosmological constants. An important contribution appears due to signature change which leads to a transient rapid expansion of the bubbles in this background.Comment: 8 pages, no figure

Correspondence between Jordan-Einstein frames and Palatini-metric formalisms

We discuss the conformal symmetry between Jordan and Einstein frames considering their relations with the metric and Palatini formalisms for modified gravity. Appropriate conformal transformations are taken into account leading to the evident connection between the gravitational actions in the two mentioned frames and the Hilbert-Einstein action with a cosmological constant. We show that the apparent differences between Palatini and metric formalisms strictly depend on the representation while the number of degrees of freedom is preserved. This means that the dynamical content of both formalism is identical.Comment: 6 pages, to appear in Mod. Phys. Lett.

Classical and quantum spinor cosmology with signature change

We study the classical and quantum cosmology of a universe in which the matter source is a massive Dirac spinor field and consider cases where such fields are either free or self-interacting. We focus attention on the spatially flat Robertson-Walker cosmology and classify the solutions of the Einstein-Dirac system in the case of zero, negative and positive cosmological constant $\Lambda$. For $\Lambda<0$, these solutions exhibit signature transitions from a Euclidean to a Lorentzian domain. In the case of massless spinor fields it is found that signature changing solutions do not exist when the field is free while in the case of a self-interacting spinor field such solutions may exist. The resulting quantum cosmology and the corresponding Wheeler-DeWitt equation are also studied for both free and self interacting spinor fields and closed form expressions for the wavefunction of the universe are presented. These solutions suggest a quantization rule for the energy.Comment: 13 pages, 4 figure

On Signature Transition and Compactification in Kaluza-Klein Cosmology

We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative cosmological constant and a Robertson-Walker type metric. It is shown that the solutions to Einstein field equations have degenerate metric and exhibit transitioins from a Euclidean to a Lorentzian domain. We then suggest a mechanism, based on signature transition which leads to compactification of the internal space in the Lorentzian region as $a \sim |\Lambda|^{1/2}$. With the assumption of a very small value for the cosmological constant we find that the size of the universe $R$ and the internal scale factor $a$ would be related according to $Ra\sim 1$ in the Lorentzian region. The corresponding Wheeler-DeWitt equation has exact solution in the mini-superspace giving rise to a quantum state which peaks in the vicinity of the classical solutions undergoing signature transition.Comment: 13 pages, 3 figure

Risk assessment of hot and humid environments through an integrated fuzzy AHP-VIKOR method

Working in hot and humid environments can jeopardize the health and safety of the workers and reduce their efficiency. Different physical, environmental, and human factors can influence the risk level of working in these atmospheres. Therefore, the risk assessment of such atmospheres must be carried out from a holistic point of view. This paper aims to introduce a novel risk assessment and prioritization model, using hybrid AHP and VIKOR methods in a fuzzy environment. The AHP method was adopted to determine the importance (weight) of the risk influencing parameters. Also, the VIKOR as a compromise solution method was applied to rank the different working stations against the risk criteria. Fuzzy set theory was used to handle the inherent ambiguity and vagueness of the data encountered in the evaluation process. Furthermore, the fuzzy TOPSIS was adopted to further represent the efficacy of the proposed model. To demonstrate the applicability of the model, a small size foundry shop was selected as the real case and a sensitivity analysis was performed to confirm the validity of the model. The results revealed that the “Environment” has the most contribution to the risk level of hot environments (WE = 0.615). That is followed by “Temperature” (WDBT = 0.268), “Air velocity” (WAV = 0.170), “Safety training” (WST = 0.161), “Mean radiant intensity” (WMRT = 0.110), “Humidity” (WH = 0.066), “Seniority structure” (WSS = 0.063), “Work intensity” (WWI = 0.058), “PPE” (WPPE = 0.047), “Work nature” (WPPE = 0.034), and “ Work duration” (WT = 0.022), in sub-factors. Using the F-VIKOR method, the “melting furnace” workstation was determined as the compromise solution with the index value of Q = 1

Computing ?-Stretch Paths in Drawings of Graphs

Let f be a drawing in the Euclidean plane of a graph G, which is understood to be a 1-dimensional simplicial complex. We assume that every edge of G is drawn by f as a curve of constant algebraic complexity, and the ratio of the length of the longest simple path to the the length of the shortest edge is poly(n). In the drawing f, a path P of G, or its image in the drawing ?=f(P), is ?-stretch if ? is a simple (non-self-intersecting) curve, and for every pair of distinct points p?P and q?P, the length of the sub-curve of ? connecting f(p) with f(q) is at most ?||f(p)-f(q)?, where ?.? denotes the Euclidean distance. We introduce and study the ?-stretch Path Problem (?SP for short), in which we are given a pair of vertices s and t of G, and we are to decide whether in the given drawing of G there exists a ?-stretch path P connecting s and t. The ?SP also asks that we output P if it exists. The ?SP quantifies a notion of "near straightness" for paths in a graph G, motivated by gerrymandering regions in a map, where edges of G represent natural geographical/political boundaries that may be chosen to bound election districts. The notion of a ?-stretch path naturally extends to cycles, and the extension gives a measure of how gerrymandered a district is. Furthermore, we show that the extension is closely related to several studied measures of local fatness of geometric shapes. We prove that ?SP is strongly NP-complete. We complement this result by giving a quasi-polynomial time algorithm, that for a given ?>0, ??O(poly(log |V(G)|)), and s,t?V(G), outputs a ?-stretch path between s and t, if a (1-?)?-stretch path between s and t exists in the drawing