Measuring the Double Layer Capacitance of Electrolytes with Varied Concentrations

When electric potentials are applied from an electrolytic fluid to a metal, a double layer capacitor, Cdl, develops at the interface. The layer directly at the interface is called the Stern layer and has a thickness equal to roughly the size of the ions in the fluid. The next layer, the diffuse layer, arises from the gathering of like charges in the Stern layer. This layer is the distance needed for ionic concentrations to match the bulk fluid. This distance, called the Debye length, λ, depends on the square root of the electrolyte concentration. To study the properties of the diffuse layer, we measure C using different concentrations of electrolyte solutions in a cylindrical capacitor system we machined

Comment on: Measuring non-Hermitian operators via weak values [A.K.Pati, U Singh and U. Sinha, Phys.Rev.A92,052120 (2015), arXiv:1406.3007]

We notice that the 5-parameter matrix and the corresponding wave functions ,fail to satisfy the eigenvalue condition or relation reported earlier in this journal in ,Phys.Rev. A 92,052120(2015) .Comment: English corrections only and typographical mistake

Some studies on quantum equivalents of non-commutative operators via commutating eigenvalue relation: PT-symmetry

We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This universality relation is also equally valid for any matrix in any branch of physical or social science and also any operator involving co-ordinate$(x)$ or momentum$(p)$. Pictorially this is represented in fig. 1. Many interesting models including logarithmic potential have been considered.Comment: Since new submissions are not allowed, I have replaced my previous article, which may kindly be allowe

A short proof of the phase transition for the vacant set of random interlacements

The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories, where $u$ is a parameter controlling the density of the cloud. It was proved in arXiv:0704.2560 and arXiv:0808.3344 that for any $d \geq 3$ there exists a positive and finite threshold $u_*$ such that if $u<u_*$ then the vacant set percolates and if $u>u_*$ then the vacant set does not percolate. We give an elementary proof of these facts. Our method also gives simple upper and lower bounds on the value of $u_*$ for any $d \geq 3$.Comment: 11 pages, 1 figure; Title of paper change