Charged Cylinder Research Articles

Models of Collapsing and Expanding Cylindrical Source in f(R,T) Theory

We discuss the collapsing and expanding solutions of anisotropic charged cylinder in the context of f(R,T) theory (R represents the Ricci scalar and T denotes the trace of energy-momentum tensor). For this purpose, we take an auxiliary solution of Einstein-Maxwell field equations and evaluate expansion scalar whose negative values lead to collapse and positive values give expansion. For both cases, the behavior of density, pressure, anisotropic parameter, and mass is explored and the effects of charge as well as model parameter on these quantities are examined. The energy conditions are found to be satisfied for both solutions.

Hypergeometric solutions for Coulomb self-energy model of uniformly charged hollow cylinder

ABSTRACTThe article aims at studying hypergeometric-type mathematical techniques based on the extension of a model previously used to describe the Coulomb self-energy of a uniformly charged a three-dimensional cylinder. The associated crossed term integral is investigated and solved by introducing a computational series built from hypergeometric-type terms for different values of parameters involved. The approach considered may be appealing for a broad audience of researchers working in mathematical physics or related disciplines.

An analytical model for the transverse permeability of gas diffusion layer with electrical double layer effects in proton exchange membrane fuel cells

An analytical model is presented for the transverse permeability of gas diffusion layer (GDL) based on an ordered array of parallel charged circular cylinders at the steady state. The formula of calculating the permeability of the transverse direction is given by solving the fluid momentum equation in a unit cell. In the present approach, the proposed model is explicitly related to the porosity and fiber radius of fibrous porous media, the zeta potential, and the physical properties of the electrolyte solution. Besides, the effects of these parameters (the porosity, unit cell aspect ratio, fiber radius, and molar concentration) on the transverse permeability are discussed detailedly. The model predictions are compared with the previous studies in the available literature, and good agreement is found.

Rodlike Counterions near Charged Cylinders: Counterion Condensation and Intercylinder Interaction.

We study a system composed of like-charged cylinders and dumbbell-like counterions, with the focus laid on the role of the internal structure of counterions, using MonteCarlo simulations. The dumbbell ions are found to exhibit novel counterion condensation behavior governed by their length. Effective electrostatic interactions mediated between charged parallel cylinders also turn out significantly different from the case of pointlike ions, as a result of the complex interplay between the spatially separated charge distribution in the dumbbell counterions, their orientation, and the curvature of the charged cylinder. We show that at a weak-to-moderate electrostatic coupling strength, where effective like-charge interactions are usually found to be repulsive, the intercylinder interaction can become attractive and display a distinctive sensitivity to the cylinder curvature and dumbbell size, proving the significant effect of ion structure.

Interaction between Charged Cylinders in Electrolyte Solution; Excluded Volume Effect.

Electrostatic interactions govern the physical properties of charged cylindrical structures in electrolyte solutions. Besides the surface charge on the cylinders, another factor influencing the electrostatic interactions are the mobile ions. The finite size of the mobile ions is included by the excluded volume effect within the lattice statistics, while the electrostatic interactions are considered by means of the mean electrostatic field. In this article we consider charged parallel cylinders embedded into an electrolyte solution of mobile monovalent ions. A modified nonlinear Poisson-Boltzmann equation is proposed via variational procedure, and we implement the finite element method to solve it numerically. Excluded volume effect of the system containing two and multiple charged parallel cylinders are taken into account. Numerical results show that the excluded volume effect decreases the concentration of counterion and increases the electrostatic potential near the charged cylinders. The angular distribution of counterion around the particular cylinder is asymmetric. The study of the electrostatic interaction between two parallel equally charged cylinders reveals that an increase in the free energy is seen when the ionic strength is decreased. The free energy decreases as a function of the cylinders separation distance. On the contrary for two oppositely charged cylinders, the free energy increases with increasing cylinder separation distance, while for two cylinders with different charged density it shows nonmonotonic variation with the increasing cylinders separation distance.

Hidden Criticality of Counterion Condensation Near a Charged Cylinder

Counterion condensation onto a charged cylinder, known as the Manning transition, has received a great deal of attention since it is essential to understand the properties of polyelectrolytes in ionic solutions. However, the current understanding is still far from complete and poses a puzzling question: While the strong-coupling theory valid at large ionic correlations suggests a discontinuous nature of the counterion condensation, the mean-field theory always predicts a continuous transition at the same critical point. This naturally leads to a question how one can reconcile the mean-field theory with the strong-coupling prediction. Here, we study the counterion condensation transition on a charged cylinder via Monte Carlo simulations. Varying the cylinder radius systematically in relation to the system size, we find that in addition to the Manning transition, there exists a novel transition where all counterions are bound to the cylinder and the heat capacity shows a drop at a finite Manning parameter. A finite-size scaling analysis is carried out to confirm the criticality of the complete condensation transition, yielding the same critical exponents with the Manning transition. We show that the existence of the complete condensation is essential to explain how the condensation nature alters from continuous to discontinuous transition.

Scaling and criticality of the Manning transition

We consider a system consisting of a charged cylinder in the presence of neutralizing counterions. This system is well known to exhibit the Manning transition of counterion condensation onto the charged cylinder. We study the criticality and the scaling properties of the Manning transition, analyzing involved thermodynamic quantities such as condensed fraction, its fluctuation, and heat capacity. Through the Monte Carlo simulations and finite-size scaling analysis, we find that near the transition point the examined quantities exhibit scale-invariant behaviors with specific exponents, which provides an evidence that the Manning transition is a critical phenomenon having a scale-invariant property, analogous to bulk phase transitions. Furthermore, we numerically confirm that such scaling properties are not affected by the coupling strength.

Dynamical instability of a charged gaseous cylinder

In this paper, we discuss dynamical instability of charged dissipative cylinder under radial oscillations. For this purpose, we follow the Eulerian and Lagrangian approaches to evaluate linearized perturbed equation of motion. We formulate perturbed pressure in terms of adiabatic index by applying the conservation of baryon numbers. A variational principle is established to determine characteristic frequencies of oscillation which define stability criteria for gaseous cylinder. We compute the ranges of radii as well as adiabatic index for both charged and uncharged cases in Newtonian and post-Newtonian limits. We conclude that dynamical instability occurs in the presence of charge if the gaseous cylinder contracts to the radius $R_{*}$.

Cracking in charged anisotropic cylinder

In this paper, we study the stability of static charged anisotropic cylindrically symmetric compact object through cracking. The Einstein–Maxwell field equations and conservation equation are formulated. We then apply local density perturbation and study the behavior of force distribution function. Finally, the cracking is explored for two models satisfying specific form of Chaplygin equation of state. It is found that these models exhibit cracking and the instability increases as the value of charge parameter is increased.

Counterion accumulation effects on a suspension of DNA molecules: Equation of state and pressure-driven denaturation.

The study of the effects associated with the electrostatic properties of DNA is of fundamental importance to understand both its molecular properties at the single molecule level, like the rigidity of the chain, and its interaction with other charged bio-molecules, including other DNA molecules; such interactions are crucial to maintain the thermodynamic stability of the intra-cellular medium. In the present work, we combine the Poisson-Boltzmann mean-field theory with an irreversible thermodynamic approximation to analyze the effects of counterion accumulation inside DNA on both the denaturation profile of the chain and the equation of state of the suspension. To this end, we model the DNA molecule as a porous charged cylinder immersed in an aqueous solution. These thermo-electrostatic effects are explicitly studied in the particular case of some genes for which damage in their sequence is associated with diffuse large B-cell lymphoma.

Conformational properties of block-polyampholytes adsorbed on charged cylindrical surfaces.

Polyampholytes are polymers that have positive and negative monomers along their chain. The adsorption of polyampholytes on charged surfaces has been the subject of a large number of theoretical, computational and experimental studies due to its importance in a variety of bio and nanothechnological systems. However, computational studies focusing on interaction between polyampholytes and cylindrical charged surfaces are rather scarce. This study, therefore, aims to investigate the conformational properties of block-polyampholytes in the presence of a negatively charged cylinder by means of Metropolis Monte Carlo simulations. Adopting a simplified model in which the electrolyte solution is treated at the Debye-Hückel level, the effects of the ionic strength, the linear charge density of the cylinder and the block length on monomers distributions have been investigated. It was found that increasing the salt concentration promotes a transition from a conformation characterized by large loops to a necklace-like conformation parallel to the surface. It was also shown that, at low cylinder charge density, the increase in salt concentration and the length of the blocks lead to a change in the orientation of the adsorbed chain.

The tilt-dependent potential of mean force of a pair of DNA oligomers from all-atom molecular dynamics simulations

Electrostatic interactions between DNA molecules have been extensively studied experimentally and theoretically, but several aspects (e.g. its role in determining the pitch of the cholesteric DNA phase) still remain unclear. Here, we performed large-scale all-atom molecular dynamics simulations in explicit water and 150 mM sodium chloride, to reconstruct the potential of mean force (PMF) of two DNA oligomers 24 base pairs long as a function of their interaxial angle and intermolecular distance. We find that the potential of mean force is dominated by total DNA charge, and not by the helical geometry of its charged groups. The theory of homogeneously charged cylinders fits well all our simulation data, and the fit yields the optimal value of the total compensated charge on DNA to ≈65% of its total fixed charge (arising from the phosphorous atoms), close to the value expected from Manning’s theory of ion condensation. The PMF calculated from our simulations does not show a significant dependence on the handedness of the angle between the two DNA molecules, or its size is on the order of . Thermal noise for molecules of the studied length seems to mask the effect of detailed helical charge patterns of DNA. The fact that in monovalent salt the effective interaction between two DNA molecules is independent on the handedness of the tilt may suggest that alternative mechanisms are required to understand the cholesteric phase of DNA.

A general realistic treatment of the disk paradox

Mechanical angular momentum is not conserved in systems involving electromagnetic fields with non-zero electromagnetic field angular momentum. Conservation is restored only if the total (mechanical and field) angular momentum is considered. Previous studies have investigated this effect, known as ‘Feynman’s Electromagnetic Paradox’ or simply ‘Disk Paradox’ in the context of idealized systems (infinite or infinitesimal solenoids and charged cylinders etc). In the present analysis we generalize previous studies by considering more realistic systems with finite components and demonstrating explicitly the conservation of the total angular momentum. This is achieved by expressing both the mechanical and the field angular momentum in terms of charges and magnetic field fluxes through various system components. Using this general expression and the closure of magnetic field lines, we demonstrate explicitly the conservation of total angular momentum in both idealized and realistic systems (finite solenoid concentric with two charged cylinders, much longer than the solenoid) taking all the relevant terms into account including the flux outside of the solenoid. This formalism has the potential to facilitate a simpler and more accurate demonstration of total angular momentum conservation in undergraduate physics electromagnetism laboratories.

Formation of ordered structures in systems of charged thin cylindrical grains

Conditions for the formation of various orientational and spatial configurations of charged cylindrical particles in an external electric field are investigated both analytically and numerically. Analytical expressions allowing one to determine the tilt angle of cylinders relative to the symmetry axis/plane of the electric trap are proposed. A new algorithm for numerical modeling of the dynamics of interacting nonspherical particles is developed. Conditions for correct modeling of uniformly charged cylinders by means of “bipoles” consisting of two coupled point charges of the same sign are determined. The studies have been performed in a wide range of parameters close to those typical of laboratory experiments with dusty plasmas.

Electrostatic potential of mean force between two curved surfaces in the presence of counterion connectivity.

In this paper, we investigate effects of counterion connectivity (i.e., association of the counterions into a chain molecule) on the electrostatic potential of mean force (EPMF) between two similarly charged cylinder rods in a primitive model electrolyte solution by solving a classical density functional theory. The main findings include the following: (i) The counterion connectivity helps in inducing a like-charge-attractionlike (LCA-like) phenomenology even in a monovalent counterion solution wherein the LCA-like observation generally does not occur without the counterion connectivity. (ii) For divalent counterion solutions, the counterion connectivity can reinforce or weaken the LCA-like observation depending on the chain length N, and simply increases the equilibrium nearest surface separation of the rods corresponding to the minimum EPMF to nearly three times the counterion site diameter, whether N is large or small. (iii) If N is large enough, the LCA-like strength tends to be negatively correlated with the electrolyte concentration c over the entire range of the rod surface charge magnitude |σ*| considered; whereas if N drops, the correlation tends to become positive with decrease of the |σ*| value, and particularly for modest |σ*| values, the correlation relationship exhibits an extreme value phenomenon. (iv) In the case of a 1:1 electrolyte, the EPMF effects of the diameters of counterion and coion sites are similar in both situations with and without the counterion connectivity. All of these findings can be explained self-consistently by a recently proposed hydrogen-bonding style mechanism reinforced by one additional concept: flexibility of the counterion chain and the factors affecting it, like N and counterion site valence.

Three-body potential amongst similarly or differently charged cylinder colloids immersed in a simple electrolyte solution

.2D classical density functional theory (CDFT) calculations are performed for three similarly or differently charged cylinder colloids immersed in a 1 : 1 electrolyte solution. Three-body potential is extracted from the calculated grand potential information and main conclusions reached for the three-body potential are summarized as follows: (i) It is indicated that even in the electrostatic systems only involved with the 1 : 1 electrolyte solution and characterized with coupling parameters less than 1.0, wherein the Poisson–Boltzmann equation (PBE) is generally believed to be reliable, the PBE predicts the three-body potential to be in partial conflict with those calculated by the CDFT, whereas the CDFT calculations are in qualitative agreement with computer simulations in similar situations; (ii) The CDFT three-body potential is characterized with a repulsion at short distances plus an attraction even in the 1 : 1 electrolyte solution or a repulsion at large distances (depending on solution conditions) and a continuous decay to zero at longer distances, and the attraction tends to become weaker with the counter-ion diameter; (iii) Given a constant total surface charge magnitude on the three cylinder rods, the three-body potential tends to become less repulsive when the three rods are similarly charged, and conversely, tends to be less attractive when the three rods are differently charged; and (iv) When the three-rod system is differently charged, the three-body potential is relatively insensitive to the counter-ion diameter. Based on analysis of the 3D density profiles of the salt ions calculated by the CDFT, the above findings are explained by a ‘hydrogen-bond’ type mechanism augmented by an aggregation repulsion effect.

Barrier-induced dielectric counterion relaxation at super-low frequencies in salt-free polyelectrolyte solutions.

Based on the thermally activated diffusion of counterions over the barrier of the electrostatic binding potential, we construct a scaling theory for the slow dielectric response in dilute and semi-dilute polyelectrolyte solutions. The theory is based on an analytic evaluation of the mean-escape time of a single counterion from the surface of a polyelectrolyte chain and uses a variational expression for the electrostatic potential of a charged cylinder including counterion condensation. This mean-escape time shows a range of characteristic power-law dependencies on the polyelectrolyte length and the polyelectrolyte monomer concentration. The existence of this novel dielectric mode at super-low frequencies reflects the wide spectrum of experimental findings for the super-low-frequency dielectric relaxation mode and thereby helps to reconcile conflicting interpretations of experimental data in terms of conventional scaling laws. We also devise a scaling theory for the counterion condensation of finite-length polyelectrolyte chains at finite concentration, which allows us to include polyelectrolyte charge renormalization in dilute as well as semi-dilute solutions in a unified theoretical framework.

Combustion simulation and key parameter optimization for opposite axial piston engine in small-scale

As potential alternative power sources used in portable electric generators, opposite axial piston engines in small-scale were investigated to show their advantages in power density. A novel cylinder charge system was introduced, based on which a quasi-dimension model and a CFD (computational fluid dynamics) model were established. Comparison of those two models was carried out to validate the quasi-dimension model. Furthermore, optimal diameter of charge cylinder and speed were determined after evaluating the quasi-dimension model based on different parameters. High agreement between the quasi-dimension model and the CFD model validates the quasi-dimension model. Further studies show that the power of engine increases with the diameter of charge cylinder. However, a too big charge cylinder lowers the fuel efficiency instead. Taking economic influence into consideration the charge cylinder should be 1.4 times power cylinder, which could ensure the power density, volumetric efficiency and fuel economic at the same time. Axial piston engine running at 1.0×104 r/min could achieve a better overall performance. The maximal power of engine with optimal parameters is 0.82 kW, which fits the power need of the portable electric generators completely.

Asymptotic formulae for the interaction force and torque between two charged parallel cylinders

The electrostatic interactions between charged particles immersed in an ionic solution play an important role for the stability of colloidal dispersions. The distribution of the electrostatic potential in the continuous phase obeys the nonlinear Poisson–Boltzmann equation. This study aims to calculate the asymptotic expressions for the interaction force and torque between two parallel charged cylinders at large distances between them. The exact formulae obtained are expressed in terms of the modified Bessel function of the second kind. From the general physical principles two theorems about the interaction energy and the stability of the quasi-equilibrium states for multipole–multipole interactions are proved.

Experimental Analysis of a Compressed Air Engine

Nowadays, automobiles consume a large number of fossil fuels. However, the consumption of fossil fuels has brought many serious environmental problems, such as global warming, ozone layer depletion and fine particulate matter. To avoid such environmental problems, renewable energy has been applied to automobiles. In this paper, an air-powered engine of a renewable energy vehicle is introduced. To lay a foundation for the optimization of compressed air engine (CAE), a physical model of compressed air engine (CAE) is established with cam which controls compressed air charge or discharge cylinder. To obtain performance of the CAE, a prototype CAE system is set up. The output torque, power and efficiency are obtained through experimental study. The results show that the prototype of CAE has a good economic performance under low speed and when the supply pressure is 2 MPa, the maximum output power is 1.92 kW; the maximum output torque is 56.55 N·m; and the maximum efficiency is 25%. This research can be referred to in the optimization of air-powered engine.