Reconstructing inflation in scalar-torsion $$f(T,\phi )$$ gravity

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function $$f(T,\phi )$$ f ( T , ϕ ) of the torsion scalar T of teleparallel gravity and the inflaton $$\phi $$ ϕ . For the class of theories with Lagrangian density $$f(T,\phi )=-M_{pl}^{2} T/2 - G(T) F(\phi ) - V(\phi )$$ f ( T , ϕ ) = - M pl 2 T / 2 - G ( T ) F ( ϕ ) - V ( ϕ ) , with $$G(T)\sim T^{s+1}$$ G ( T ) ∼ T s + 1 and the power s as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) and the scalar potential $$V(\phi )$$ V ( ϕ ) through the parametrization (or attractor) of the scalar spectral index $$n_{s}(N)$$ n s ( N ) and the tensor-to-scalar ratio r(N) as functions of the number of $$e-$$ e - folds N. As specific examples, we analyze the attractors $$n_{s}-1 \propto 1/N$$ n s - 1 ∝ 1 / N and $$r\propto 1/N$$ r ∝ 1 / N , as well as the case $$r\propto 1/N (N+\gamma )$$ r ∝ 1 / N ( N + γ ) with $$\gamma $$ γ a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function $$F(\phi )$$ F ( ϕ ) and the potential $$V(\phi )$$ V ( ϕ ) , as also the constraints on the parameters present in our model and its reconstruction.

Biosequestration of chromium (VI) from aqueous medium using carbonaceous adsorbents derived from Eichhornia crassipes

Utilization of the biochar that are derived from Eichhornia crassipes (water hyacinth) as biosorbent for Cr (VI) adsorption was investigated. The biochar was characterized before and after Cr (VI) adsorption by SEM, FTIR and EDX. The influencing parameters viz., solution pH, solute concentrations, reaction duration, adsorbent dose and size have been examined. The most favorable conditions for Cr (VI) removal were found to be pH = 2.0, adsorbent size = 0.2 mm, adsorbent dosage = 2.5g/100ml, adsorbate/solute concentration = 100mg/L of Cr (VI) at 25ºC at 250 rpm. Rate of adsorption was rapid and equilibrium was reached at 36 hours. The equilibrium relationship between the sorbent and sorbate was determined using the isotherms Langmuir, Freundlich and Temkin models. The Langmuir dimensionless constant (KR) for each of the solute concentration was ranged between 0 and 1, it indicates the favourable adsorption of Cr (VI) onto the adsorbent. Adsorption data was very well explained through Langmuir isotherm where sorption occurs on monolayer with the maximum biosorption capacity of 55.55 mg/g. Adsorption rate and its mechanisms were elucidated through kinetic studies viz., Pseudo first order, second order, elovich and intra particle diffusion models. On comparison with various kinetic models, results fitted excellently with pseudo second order model (R2 = 0.999). It suggests that Cr (VI) adsorption by could be better described by chemisorption which involves sharing of electrons between adsorbents and adsorbate. Hence, the biochar derived from E. crassipes are efficiently used as an ecofriendly biosorbent for the management of Cr (VI) rich waste water.

Silicon Self-Diffusion in Stishovite: Calculations of Point Defect Parameters Based on the cBΩ Thermodynamic Model

In the present work we apply the cBΩ thermodynamic model to study the diffusion of Si in stishovite crystal at high pressure and in a wide temperature range. According to this model, the point defect activation Gibbs free energy is expressed as a function of the bulk properties of the material, i.e., gact = cBΩ, where B is the isothermal bulk modulus, Ω is the mean atomic volume, and c is a dimensionless constant. In this way, other important point defect parameters, such as the activation volume vact, the activation entropy sact, and the activation enthalpy hact may be estimated if the thermoelastic properties of the material are known over a wide temperature and pressure range. Our calculations are based on previously reported self-diffusion coefficients in stishovite single crystals measured at 14 GPa and at temperatures from 1400 to 1800 °C, in the [110] and [001] directions, by Shatskiy et al. (Am. Mineral. 2010, 95, 135–43). Furthermore, the EOS of stishovite, proposed by Wang et al. (J. Geophys. Res. 2012, 117, B06209) has been used for the accurate implementation of the cBΩ model. Our results suggest that the aforementioned point defect parameters exhibit considerable temperature dependence over the studied temperature range (1000–2000 °C). The estimated activation volumes (4.4–5.3 cm3/mol, in the range of 1400–1800 °C) are in agreement with reported experimental results. Our study confirms the potential of the cBΩ model for the theoretical investigation of diffusion processes in minerals, in order to overcome the experimental difficulties and the lack of experimental diffusion data in mantle conditions.

Speed of sound from fundamental physical constants

Two dimensionless fundamental physical constants, the fine structure constant α and the proton-to-electron mass ratio mpme, are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant that provides the upper bound for the speed of sound in condensed phases, vu. We find that vuc=α(me2mp)12, where c is the speed of light in vacuum. We support this result by a large set of experimental data and first-principles computations for atomic hydrogen. Our result expands the current understanding of how fundamental constants can impose new bounds on important physical properties.

An EGD model in the background of embedding class I space–time

This work is devoted to the study of relativistic anisotropic compact objects. To obtain this class of solutions of the Einstein field equations, we have developed a general scheme to generate the metric of the space–time describing the interior of the compact structure. This approach is based on the class I space–time and the extended gravitational decoupling by means of an extended geometric deformation (EGD). The class I condition provides a differential equation relating both metric potential $$\nu $$ ν and $$\lambda $$ λ , whilst the EGD translates the metric potentials to $$ \nu =\xi +\beta \,h(r)$$ ν = ξ + β h ( r ) and $$ \lambda =-\ln [\mu +\beta \,f(r)]$$ λ = - ln [ μ + β f ( r ) ] , where h(r) and f(r) are the deformation functions and $$\beta $$ β a dimensionless constant. In this case the pair $$\{\xi ,\mu \}$$ { ξ , μ } represents the seed solution satisfying the class I condition without any deformation. Once the deformed metric potentials are inserted into the class I, the main task is to obtain h(r) or f(r). So, in this case a particular ansatz for h(r) is considered in conjunction with $$\beta =0.5$$ β = 0.5 to get f(r). In order to check feasibility of our model, we have performed a thoroughly physical, mathematical and graphical analysis.

Oбобщенный кинетический критерий перехода жидкость--стекло

Using the model of delocalized atoms, a substantiation and generalization of the Schmelzer glass transition criterion is proposed. In contrast to the Bartenev and Volkenstein - Ptitsyn approaches, in the generalized kinetic glass transition criterion, along with the relaxation time and the cooling rate of the melt, the glass transition temperature and an almost universal dimensionless constant appear, which is determined by the fraction of the fluctuation volume frozen at the glass transition temperature. The idea is developed that the liquid goes into a glassy state when its cooling rate q reaches a certain fraction of C_g of the characteristic cooling rate q_g=(T_g/taug), which is closely related to the relaxation time of the structure tau_g at the glass transition temperature T_g.

A New Unified Electro-Gravity Theory for the Electron

A rigorous model for the electron is presented by generalizing the Coulomb's Law or Gauss's Law of electrostatics, using a unified theory of electricity and gravity. The permittivity of the free-space is allowed to be variable, dependent on the energy density associated with the electric field at a given location, employing generalized concepts of gravity and mass/energy density. The electric field becomes a non-linear function of the source charge, where concept of the energy density needs to be properly defined. Stable solutions are derived for a spherically symmetric, surface-charge distribution of an elementary charge. This is implemented by assuming that the gravitational field and its equivalent permittivity function is proportional to the energy density, as a simple first-order approximation, with the constant of proportionality referred to as the Unifield Electro-Gravity (UEG) constant. The stable solution with the lowest mass/energy is assumed to represent a ``static'' electron without any spin. Further, assuming that the mass/energy of a static electron is half of the total mass/energy of an electron including its spin contribution, the required UEG constant is estimated. More fundamentally, the lowest stable mass of a static elementary charged particle, its associated classical radius, and the UEG constant are related to each other by a dimensionless constant, independent of any specific value of the charge or mass of the particle. This dimensionless constant is numerologically found to be closely related to the the fine structure constant. This possible origin of the fine structure constant is further strengthened by applying the proposed theory to successfully model the Casimir effect, from which approximately the same above relationship between the UEG constant, electron's mass and classical radius, and the fine structure constant, emerges.

Variables Affecting Nut Factors in Bolted Flange Connections

Bolted flange connections are heavily used within the chemical production/processing, transportation, marine, and power generation industries to contain processes while minimizing leaks. These leaks could cause unsafe working conditions, environmental hazards, and/or loss of product which, in turn, can cause fines or higher operating cost for plants. A way to deter this from happening is to correctly load the fasteners of the bolted flange connections to ensure the fasteners are properly stretched to apply an adequate contact stress to the gasket. Good understanding of how bolted flanged connections are optimally loaded limits leakage. When applying load via controlled torque to a fastener, the torsional energy applied is translated into a perpendicular force acting on the nut’s face and threads that is mirrored on the other side of the fastener thus inducing the clamping force on the connection. To determine the clamping force generated from the applied torque, a typical torque equation is applied using an empirically derived composite friction term called the nut factor. The nut factor is a dimensionless constant that includes all of the friction effects in the torque-clamping force relationship. The friction occurs between the surfaces of bolt and nut threads and the faces of the nut and flange or washer. The higher the friction, the higher the nut factor resulting in a higher fastener torque to achieve the same clamping force load. This study looked at several variables that can cause changes in assembly nut factor magnitude including bolt grade, bolt load, lubrication, washer presence, and bolt diameter.

A New Unified Electro-Gravity Theory for the Electron

A rigorous model for an electron is presented by generalizing the Coulomb's Law or Gauss's Law of electrostatics, using a unified theory of electricity and gravity. The permittivity of the free-space is allowed to be variable, dependent on the energy density associated with the electric field at a given location, employing generalized concepts of gravity and mass/energy density. The electric field becomes a non-linear function of the source charge, where concept of the energy density needs to be properly defined. Stable solutions are derived for a spherically symmetric, surface-charge distribution of an elementary charge. This is implemented by assuming that the gravitational field and its equivalent permittivity function is proportional to the energy density, as a simple first-order approximation, with the constant of proportionality referred to as the Unifield Electro-Gravity (UEG) constant. The stable solution with the lowest mass/energy is assumed to represent a ``static'' electron without any spin. Further, assuming that the mass/energy of a static electron is half of the total mass/energy of an electron including its spin contribution, the required UEG constant is estimated. More fundamentally, the lowest stable mass of a static elementary charged particle, its associated classical radius, and the UEG constant are related to each other by a dimensionless constant, independent of any specific value of the charge or mass of the particle. This dimensionless constant is numerologically suspected to be closely related to the the fine structure constant. This finding may carry greater fundamental significance, with scope of the UEG theory covering other elementary particles in the standard model of particle physics.

A Study of Earthquake Recurrence based on a One-body Spring-slider Model in the Presence of Thermal-pressurized Slip-weakening Friction and Viscosity

Earthquake recurrence is studied from the temporal variation in slip through numerical simulations based on the normalized equation of motion of a one-body spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity. The major model parameters are the normalized characteristic displacement, Uc, of the friction law and the normalized damping coefficient (to represent viscosity), η. Simulation results exhibit that both friction and viscosity remarkably affect slip of the slider. The recurrence time, TR, increases with η or with decreasing Uc. The final slip, D, and the duration time of slip, τD, of an event decrease with increasing η; while τD increases with Uc. The time-predictable and slip-predictable models can describe the temporal variation in cumulative slip. Considering the effect caused by wear process, the thickness of slip zone, h, depends on the cumulated slip, S(t) = ∑D(t): h(t) = CS(t) where C is a dimensionless constant. Uc is a function of h and thus influenced by C. In the computational time period, when C 0.0001 the wear process influences the slip recurrence and its effect increases with C. Neither the time-predictable model nor the slip-predictable model can describe the temporal variation in cumulative slip when the wear process with high C works.