Shadow and deflection angle of charged rotating black hole surrounded by perfect fluid dark matter

We analysed the shadow cast by charged rotating black hole (BH) in presence of perfect fluid dark matter (PFDM). We studied the null geodesic equations and obtained the shadow of the charged rotating BH to see the effects of PFDM parameter $\gamma$, charge $Q$ and rotation parameter $a$, and it is noticed that the size as well as the shape of BH shadow is affected due to PFDM parameter, charge and rotation parameter. Thus, it is seen that the presence of dark matter around a BH affects its spacetime. We also investigated the influence of all the parameters (PFDM parameter $\gamma$, BHs charge $Q$ and rotational parameter $a$) on effective potential, energy emission by graphical representation, and compare all the results with the non rotating case in usual general relativity. To this end, we have also explored the effect of PFDM on the deflection angle and the size of Einstein rings.

Emergent spatiotemporal population dynamics with cell-length control of synthetic microbial consortia

The increased complexity of synthetic microbial biocircuits highlights the need for distributed cell functionality due to concomitant increases in metabolic and regulatory burdens imposed on single-strain topologies. Distributed systems, however, introduce additional challenges since consortium composition and spatiotemporal dynamics of constituent strains must be robustly controlled to achieve desired circuit behaviors. Here, we address these challenges with a modeling-based investigation of emergent spatiotemporal population dynamics using cell-length control in monolayer, two-strain bacterial consortia. We demonstrate that with dynamic control of a strain’s division length, nematic cell alignment in close-packed monolayers can be destabilized. We find that this destabilization confers an emergent, competitive advantage to smaller-length strains—but by mechanisms that differ depending on the spatial patterns of the population. We used complementary modeling approaches to elucidate underlying mechanisms: an agent-based model to simulate detailed mechanical and signaling interactions between the competing strains, and a reductive, stochastic lattice model to represent cell-cell interactions with a single rotational parameter. Our modeling suggests that spatial strain-fraction oscillations can be generated when cell-length control is coupled to quorum-sensing signaling in negative feedback topologies. Our research employs novel methods of population control and points the way to programming strain fraction dynamics in consortial synthetic biology.

Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles

The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

Emergent spatiotemporal population dynamics with cell-length control of synthetic microbial consortia

Increased complexity of engineered microbial biocircuits highlights the need for distributed cell functionality due to concomitant increases of metabolic and regulatory burdens imposed on single-strain topologies. Distributed systems, however, introduce additional challenges since consortium composition and spatiotemporal dynamics of constituent strains must be robustly controlled to achieve desired circuit behaviors. Here, we address these challenges with a modeling-based investigation of emergent spatiotemporal population dynamics that result from cell-length control of monolayer, two-strain bacterial consortia. We demonstrate that with dynamic control of a strain's division length, nematic cell alignment in close-packed monolayers can be destabilized. We found this destabilization conferred an emergent, competitive advantage on smaller-length strains---but by mechanisms that differed depending on the spatial patterns of the population. We used complementary modeling approaches to elucidate underlying mechanisms: an agent-based model to simulate detailed mechanical and signaling interactions between the competing strains and a reductive, stochastic lattice model to represent cell-cell interactions with a single rotational parameter. Our modeling suggests that spatial strain-fraction oscillations can be generated when cell-length control is coupled to quorum-sensing signaling in negative feedback topologies. Our research employs novel methods of population control and points the way to programming strain fraction dynamics in consortial synthetic biology.

Holographic drag force in 5d Kerr-AdS black hole

We consider the 5d Kerr-AdS black hole as a gravity dual to rotating quark-gluon plasma. In the holographic prescription we calculate the drag force acting on a heavy quark. According to the holographic approach a heavy quark can be considered through the string in the gravity dual. We study the dynamics of the string for the Kerr-AdS backgrounds with one non-zero rotational parameter and two non-zero rotational parameters that are equal in magnitude. For the case of one non-zero rotational parameter we find good agreement with the prediction from the 4d case considered by arXiv:1012.3800.

Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field

The propagation of a cylindrical shock wave in rotating medium with azimuthal magnetic field under the action of monochromatic radiation using a method of group invariance is investigated. To derive similarity solutions as well as exact solutions, the group invariance technique is used. All classes of the solutions depending on the absorption coefficient are discussed by considering absorption coefficient to be variable or constant. A similarity solution is obtained, when the absorption coefficient is assumed to be variable. Two cases of solutions with a power law shock path are obtained by the different choices of arbitrary constants involving in the infinitesimal generators of the Lie group of transformations. To obtain the similarity solution in the case of the power law shock path, the density, magnetic field, axial and azimuthal velocity components are assumed to be varying and obeying power laws in the undisturbed medium. It is observed that with increase in the values of Alfven Mach number, adiabatic exponent and rotational parameter, shock strength decreases. The effects of variation of magnetic field strength, adiabatic exponent, rotational parameter and initial magnetic field variation index on the flow variables and on shock waves are analyzed graphically. Also, all classes of exact solutions are obtained by considering a constant absorption coefficient.

Effects of Chemical Reaction, Activation Energy and Thermal Energy on Magnetohydrodynamics Maxwell Fluid Flow in Rotating Frame

The purpose of this research is to see how chemical processes, activation energy, and heat radiation affect MHD flow of Maxwell fluid in a rotating frame. Using applicable similarity transformations, the partial differential equations that regulate the flow are reduced to extremely nonlinear ordinary differential equations. Graphs and tables are used to study the impact of monitoring parameters on velocity, temperature, concentration profiles, reduced Nusselt number, reduced Sherwood numbers, and skin friction coefficients. Outstanding agreement is obtained when the present findings of the study is compared with the previous related research works. In the study, it is noted that an increase of the thermal radiation parameters contributes to an increase of the flow temperature region. When a fluid is subjected to a greater rotation parameter, the thermal boundary layer thickens and the heat transfer rate decrease. Moreover, a decline of mass transfer rate is observed for a rise of Prandl number, rotational parameter or Deborah number.

Magnetic Rotating Flow of a Hybrid Nano-Materials Ag-MoS2 and Go-MoS2 in C2H6O2-H2O Hybrid Base Fluid over an Extending Surface Involving Activation Energy: FE Simulation

Numeric simulations are performed for a comparative study of magnetohydrodynamic (MHD) rotational flow of hybrid nanofluids (MoS2-Ag/ethyleneglycol-water (50–50%) and MoS2-Go/ethyleneglycol-water (50–50%)) over a horizontally elongated plane sheet. The principal objective is concerned with the enhancement of thermal transportation. The three-dimensional formulation governing the conservation of mass, momentum, energy, and concentration is transmuted into two-dimensional partial differentiation by employing similarity transforms. The resulting set of equations (PDEs) is then solved by variational finite element procedure coded in Matlab script. An intensive computational run is carried out for suitable ranges of the particular quantities of influence. The primary velocity component decreases monotonically and the magnitude of secondary velocity component diminishes significantly when magnetic parameter, rotational parameter, and unsteadiness parameter are incremented. Both the primary and secondary velocities are smaller in values for the hybrid phase Ag-MoS2 than that of hybrid phase Go-MoS2 but the nanoparticle concentration and temperature are higher for hybrid phase Ag-MoS2. The increased values of parameters for thermophoresis, Brownian motion, shape factor, and volume fraction of ϕ2 made significant improvement in the temperature of the two phases of nano liquids. Results are also computed for the coefficients of skin friction(x, y-directions), Nusselt number, and Sherwood number. The present findings manifest reasonable comparison to their existing counterparts. Some of the practical engineering applications of the present analysis may be found in high-temperature nanomaterial processing technology, crystal growing, extrusion processes, manufacturing and rolling of polymer sheets, academic research, lubrication processes, and polymer industry.

Analysis of entropy generation minimization (EGM) in flow of Ree-Eyring nanofluid between two coaxially rotating disks

The present communication addresses MHD radiative nanomaterial flow of Ree-Eying fluid between two coaxially rotating disks. Both disks are stretchable. Buongiorno model is used for nanofluids. Nanofluid aspects comprise random motion of particles (Brownian diffusion) and thermophoresis. MHD fluid is considered. Furthermore, dissipation, radiative heat flux and Ohmic heating effects are considered to model the energy equation. Total entropy rate is calculated through implementation of second thermodynamics law. Series solutions are developed through homotopy analysis method. Impacts of physical parameters on the velocity, temperature, entropy and concentration fields are discussed graphically. Skin friction coefficient and heat and mass transfer rates are numerically calculated through Tables 2-4. It is noticed that the velocity of liquid particles decreases versus higher estimations of magnetic parameter while it enhances via larger rotational parameter. Temperature field significantly increases in the presence of both Brownian diffusion and thermophoresis parameters.