Thermodynamic instability of topological black holes with nonlinear source

In this paper, we obtain higher dimensional topological black hole solutions of Einstein-$\Lambda$ gravity in the presence of a class of nonlinear electrodynamics. First, we calculate the conserved and thermodynamic quantities of ($n+1$)-dimensional asymptotically flat solutions and show that they satisfy the first law of thermodynamics. Also, we investigate the stability of these solutions in the (grand) canonical ensemble. Second, we endow a global rotation to the static Ricci-flat solutions and calculate the conserved quantities of solutions by using the counterterm method. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Then, we perform a stability analysis of the rotating solutions both in the canonical and the grand canonical ensembles.Comment: 17 pages with 14 figures, accepted in EPJ

A new approach toward geometrical concept of black hole thermodynamics

Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity.Comment: 13 pages with 7 figures, accepted in EPJ

The benefits of fish and rice integrated culture in Iran

Fish culture in rice field is an ancient activity in Asia and probably it has been a routine activity in China since decades ago. Countries are now gradually finding out the advantages of the activity putting more and more land under the integrated culture. The integrated culture was first conducted in 1983 in Iran. Since then, the activity has been extended in the rice fields of 11 provinces of the country. In an experimental project in 2003, 13 rice fields totally covering 8.2 hectares and 13 control fields with the same size, physical and chemical conditions were chosen to investigate the outcomes of the integrated culture. For this, 1400 specimens of juvenile fish each weighting on average 3545 grams and composed of 57% common cam, 29 % grass carp, 14% silver carp and big head carp were stocked per hectare of each field. The average weight for grass catty individuals was 25-35 grams. Feeding rate was based on the fish biomass. In harvesting time, characteristics of the rice were compared between experimental and control fields in order to determine the quality and quantity changes in the product. At the same time, usage of fertilizer, pesticides and herbicides were measured in both experimental and control fields. The pesticide usage in control fields was 15 kg per hectare, but in experimental fields it was only 5kg per hectare. This showed 66% reduction in pesticide use. In each control field, 2 liters of herbicides was used, as compared to only 0.3 liter per hectare in the experimental fields, showing an 85% percent reduction. The chemical fertilizer (urea, phosphate, potassium) used in the control fields was 169 kg per hectare, translating into a 23% reduction in each experimental field. Overall, rice production increased 302 kg per hectare in the control fields. In this experiment, the profit of fish and rice integrated farming was estimated to be 4,300,000 Rials (US$505). The results showed that enhancing fish and rice integrated farming might increase farmers' profits; while reducing the need to apply fertilizers and pesticides

Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow

Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate thermal stability conditions for these black hole solutions in context of canonical ensemble. We show that thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge and energy functions.Comment: 13 pages, 5 figure

Three dimensional nonlinear magnetic AdS solutions through topological defects

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known BornInfeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and in other words, we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appear too.Comment: 22 pages with 24 figures. Accepted for publication in Eur. Phys. J.

An investigation on species composition and quantitative distribution of periphyton in Anzali Lagoon

The goal of study was to recognize species and distribution of periphytons in the Anzali lagoon. Periphytons are ecologically placed as a ring in biological chain between planktons and benthos. They play an important filtering role in aquatic ecosystem. Fish fry of sturgeons, kutum (Rutilus frisii kutum), and many other species feed on them. The study was carried out at eleven station, in different places of Anzali Lagoon from June to January in 1996. 176 plant and 17 animal species were recognized. Plant species were consisted of 4 phylum; Chrysophyta (69 species), Chlorophyta (52 species), Cyanophyta (48 species) and Rhodophyta (7 species). Animal species of 8 phylum, Annelida (3 species), Arthropoda (4 species), Bryozoa (3 species), Coelenterata (1 species), Mollusca (2 species), Protozoa (2 species), Kamptozoa (1 species) and Nematoda (1 species) were also recognized. Replacement of animal and plant species was observed in all stations except station 4 (the nearest place to the sea) where animal species were dominant. Study on marine factors showed that Dreissena polymorpha was more dominant and had a high biomass. To continuation of monthly sampling, making dynamic data bank and formation of Periphyton colonies, we can get more precise and more comprehensive informations on dispersion, combination and growth speed of this group of creatures in Anzali lagoon