Quantum Phase in Nanoscopic Superconductors

Using the pseudospin representation and the SU(2) phase operators we introduce a complex parameter to characterize both infinite and finite superconducting systems. While in the bulk limit the parameter becomes identical to the conventional order parameter, in the nanoscopic limit its modulus reduces to the number parity effect parameter and its phase takes discrete values. We evaluate the Josephson coupling energy and show that in bulk superconductor it reproduces the conventional expression and in the nanoscopic limit it leads to quantized Josephson effect. Finally, we study the phase flow or dual Josephson effect in a superconductor with fixed number of electrons.Comment: 11 page

Quantum phase in nanoscopic superconductors

Using the pseudospin representation and the SU(2) phase operators we introduce a complex parameter to characterize both infinite and finite superconducting systems.While in the bulk limit the parameter becomes identical to the conventional order parameter, in the nanoscopic limit its modulus reduces to the number parity effect parameter and its phase takes discrete values. We evaluate the Josephson coupling energy and show that in bulk superconductor it reproduces the conventional expression and in the nanoscopic limit it leads to quantized Josephson effect. Finally, we study the phase flow or dual Josephson effect in a superconductor with fixed number of electrons

On Eisenstein series in M2k(Γ0(N))M_{2k}(\Gamma_0(N)) and their applications

Let $k,N \in \mathbb{N}$ with $N$ square-free and $k>1$. We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any $f(z) \in M_{2k}(\Gamma_0(N))$ in terms of sum of divisors function. In particular, if $f(z) \in E_{2k}(\Gamma_0(N))$, then the computation will to yield to an expression for the Fourier coefficients of $f(z)$. Then we apply our main theorem to give formulas for convolution sums of the divisor function to extend the result by Ramanujan, and to eta quotients which yields to formulas for number of representations of integers by certain families of quadratic forms. At last we give essential results to derive similar results for modular forms in a more general setting

Free Will: Who Can Know

I have inquired as to what sort of knowledge humans need to make justifiable claims regarding free will. I defended the thesis that humans do not have the sort of knowledge which would allow them to make such claims. Adopting the view of mind based on cognitive science and Kant’s philosophy of mind, first I laid out the characteristics of that knowledge with the help of a simulation example I devised. Then, upon investigating the epistemic relations between the different sources of knowledge and the agents of a system (such as the relation between the programmer and the simulated agents as well as god and humans), I claimed that knowledge bearing those characteristics cannot be accessible to human beings

Design of anisotropic plates for improved damage tolerance

An analytical study is presented showing the effects of the notch tip geometry on the location and direction of crack growth from an existing notch in a unidirectional fibrous composite modeled as a homogeneous, anisotropic, elastic material. Anisotropic elasticity and the normal stress ratio theory are used to study crack growth from elliptical notches in unidirectional composites. Sharp cracks, circular holes, and ellipses are studied under far-field tension and shear loading. The capabilities of a previously developed design code was upgraded to handle more generalized plate geometries and laminates under a more generalized loading and boundary conditions. Discussion of the developments of the design code is presented

Bayesian models and algorithms for protein beta-sheet prediction

Prediction of the three-dimensional structure greatly benefits from the information related to secondary structure, solvent accessibility, and non-local contacts that stabilize a protein's structure. Prediction of such components is vital to our understanding of the structure and function of a protein. In this paper, we address the problem of beta-sheet prediction. We introduce a Bayesian approach for proteins with six or less beta-strands, in which we model the conformational features in a probabilistic framework. To select the optimum architecture, we analyze the space of possible conformations by efficient heuristics. Furthermore, we employ an algorithm that finds the optimum pairwise alignment between beta-strands using dynamic programming. Allowing any number of gaps in an alignment enables us to model beta-bulges more effectively. Though our main focus is proteins with six or less beta-strands, we are also able to perform predictions for proteins with more than six beta-strands by combining the predictions of BetaPro with the gapped alignment algorithm. We evaluated the accuracy of our method and BetaPro. We performed a 10-fold cross validation experiment on the BetaSheet916 set and we obtained significant improvements in the prediction accuracy