A Time Dependent Multi-Determinant approach to nuclear dynamics

We study a multi-determinant approach to the time evolution of the nuclear wave functions (TDMD). We employ the Dirac variational principle and use as anzatz for the nuclear wave-function a linear combination of Slater determinants and derive the equations of motion. We demonstrate explicitly that the norm of the wave function and the energy are conserved during the time evolution. This approach is a direct generalization of the time dependent Hartree-Fock method. We apply this approach to a case study of ${}^6Li$ using the N3LO interaction renormalized to 4 major harmonic oscillator shells. We solve the TDMD equations of motion using Krylov subspace methods of Lanczos type. We discuss as an application the isoscalar monopole strength function.Comment: 38 pages, additional calculations included. Accepted for publication, Int. J. of Mod. Phys.

Doing Science: How to optimise patient and public involvement in your research

This paper considers how best to achieve patient and public involvement in research and how to get the most out of it http://ow.ly/R0hwV

Doing Science: How to optimise patient and public involvement in your research

This paper considers how best to achieve patient and public involvement in research and how to get the most out of it http://ow.ly/R0hw

Sum-Rate Analysis for High Altitude Platform (HAP) Drones with Tethered Balloon Relay

High altitude platform (HAP) drones can provide broadband wireless connectivity to ground users in rural areas by establishing line-of-sight (LoS) links and exploiting effective beamforming techniques. However, at high altitudes, acquiring the channel state information (CSI) for HAPs, which is a key component to perform beamforming, is challenging. In this paper, by exploiting an interference alignment (IA) technique, a novel method for achieving the maximum sum-rate in HAP-based communications without CSI is proposed. In particular, to realize IA, a multiple-antenna tethered balloon is used as a relay between multiple HAP drones and ground stations (GSs). Here, a multiple-input multiple-output X network system is considered. The capacity of the considered M*N X network with a tethered balloon relay is derived in closed-form. Simulation results corroborate the theoretical findings and show that the proposed approach yields the maximum sum-rate in multiple HAPs-GSs communications in absence of CSI. The results also show the existence of an optimal balloon's altitude for which the sum-rate is maximized.Comment: Accepted in IEEE Communications Letter

Sums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional CalculusSums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional Calculus

An attempt is made here to introduce and study a pair of double power series associated with the generalized zeta function due to Erdélyi &#934;(x; z; a) together with related sums, integral representations, generating relations and N-fractional calculus. A number of (known and new) results shown to follow as special cases of our theorems.</p

Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page