Secrecy Energy Efficiency of MIMOME Wiretap Channels with Full-Duplex Jamming

Full-duplex (FD) jamming transceivers are recently shown to enhance the information security of wireless communication systems by simultaneously transmitting artificial noise (AN) while receiving information. In this work, we investigate if FD jamming can also improve the systems secrecy energy efficiency (SEE) in terms of securely communicated bits-per- Joule, when considering the additional power used for jamming and self-interference (SI) cancellation. Moreover, the degrading effect of the residual SI is also taken into account. In this regard, we formulate a set of SEE maximization problems for a FD multiple-input-multiple-output multiple-antenna eavesdropper (MIMOME) wiretap channel, considering both cases where exact or statistical channel state information (CSI) is available. Due to the intractable problem structure, we propose iterative solutions in each case with a proven convergence to a stationary point. Numerical simulations indicate only a marginal SEE gain, through the utilization of FD jamming, for a wide range of system conditions. However, when SI can efficiently be mitigated, the observed gain is considerable for scenarios with a small distance between the FD node and the eavesdropper, a high Signal-to-noise ratio (SNR), or for a bidirectional FD communication setup.Comment: IEEE Transactions on Communication

Simulating Flows with SPH: Recent Developments and Applications

The chapter discusses recent theoretical developments and practical applications of the Smoothed Particle Hydrodynamics (SPH) method with specific concern to liquids. SPH is a meshless Lagrangian technique for the approximate integration of spatial derivatives, using particle interpolation over a compact support, without the usage of a structured grid. Its main related advantage is the capability of simulating the computational domain with large deformations and high discontinuities, bearing no numerical diffusion because advection terms are directly evaluated. SPH has recently become very popular for the simulation of fluid motion using computers, covering different fields, e.g. free surface flows, multiphase flows, turbulence modelling. In the following, recent theoretical achievements of SPH are firstly presented, concerning (1) numerical schemes for approximating governing equations, such as the Navier Stokes ones, most widely adopted in fluid dynamics, (2) smoothing or kernel function properties needed to perform the function approximation to the Nth order, (3) restoring consistency of kernel and particle approximation, yielding the SPH approximation accuracy. Secondly computation aspects related to the neighbourhood definition are discussed. Field variables, such as particle velocity or density, are evaluated by smoothing interpolation of the corresponding values over the nearest neighbour particles located inside a cut-off radius “rc”. The generation of a neighbour list at each time step takes a considerable portion of CPU time. Straightforward determination of which particles are inside the interaction range requires the computation of all pair-wise distances, a procedure whose computational time would be of the order O(N2), and therefore unpractical for large domains. Finally, some practical applications are presented, primariliy concerning free surface flows. The capability to easily handle large deformation is shown

Photoionization of few electron systems with a hybrid Coupled Channels approach

We present the hybrid anti-symmetrized coupled channels method for the calculation of fully differential photo-electron spectra of multi-electron atoms and small molecules interacting with strong laser fields. The method unites quantum chemical few-body electronic structure with strong-field dynamics by solving the time dependent Schr\"odinger equation in a fully anti-symmetrized basis composed of multi-electron states from quantum chemistry and a one-electron numerical basis. Photoelectron spectra are obtained via the time dependent surface flux (tSURFF) method. Performance and accuracy of the approach are demonstrated for spectra from the helium and berryllium atoms and the hydrogen molecule in linearly polarized laser fields at wavelength from 21 nm to 400 nm. At long wavelengths, helium and the hydrogen molecule at equilibrium inter-nuclear distance can be approximated as single channel systems whereas beryllium needs a multi-channel description

Kramers-restricted self-consistent 2-spinor fields for heavy-element chemistry

The relativistic pseudopotential (PP) method is one of the most common and successful approximations in computational quantum chemistry. If suitably parameterized -- e.g., fitted to atomic valence total energies from highly accurate relativistic reference calculations --, atomic PPs provide effective (spin�orbit) 1-electron operators mimicking the chemically inert atomic core subsystem, which thus is excluded from explicit considerations. This work deals with the development of a Kramers-restricted, 2-component PP Hartree�Fock SCF program based on the spin-restricted, 1-component HF SCF modules of the "Quantum Objects Library" of C++ program modules at the Dolg and Hanrath groups at Cologne University. Kramers' restriction, i.e. time reversal symmetry, is addressed at the lowest hierarchical level of the (formally complexified) matrix algebra modules. PP matrix elements are computed using PP integral subroutines of the ARGOS program, which are interfaced to the existing structure. On this basis, a set of spin-restricted, 1-component (all-electron and) spin-free PP, and Kramers-restricted, 2-component spin--orbit PP HF SCF programs is implemented. "Optimal damping" and initial guess density matrices constructed from atomic densities are shown to improve SCF convergence significantly. As first steps towards correlated 2-component calculation schemes, a modular structure for matrix--matrix multiplication-driven 4-index integral transformations to the Fockian eigenbasis is developed, and preliminary 2-component MP2 calculations are presented

A Multireference Density Functional Approach to the Calculation of the Excited States of Uranium Ions

An accurate and efficient hybrid Density Functional Theory (DFT)/Multireference Configuration Interaction (MRCI) model for computing electronic excitation energies in heavy element atoms and molecules was developed. This model incorporated relativistic effects essential for accurate qualitative and quantitative spectroscopic predictions on heavy elements, while simultaneously removing spin-multiplicity limitations inherent in the original model on which it is based. This model was used to successfully compute ground and low-lying electronic states for atoms in the first two rows of the period table, which were used for calibration. Once calibrated, calculations on carbon monoxide, bromine fluoride, the bromine atom, uranium +4 and +5 ions and the uranyl (UO22+) ion showed the model achieved reductions in relative error with respect to Time Dependent Density Functional Theory (TDDFT) of 11-42%, with a corresponding reduction in computational effort in terms of MRCI expansion sizes of a factor of 25-64

Quantum Criticality in Strongly Correlated Electron Systems

The study of the Hubbard model in three dimensions contains a variety of phases dependent upon the chosen parameters. This thesis shows that there is the indication of a zero temperature phase transition at a finite doping. The Hubbard model has been used to identify a similar quantum critical point in two dimensions. The presented results continue these investigations. The system demonstrates a strange metal phase at finite temperature which cannot be described in term of the conventional Fermi liquid. While there have been extensive studies over the past three decades for such materials in two dimensions, there are few numerical studies in three dimensions. This study strives to identify the existence of the strange metal beyond two dimensions. In this work we present numerical results based on the dynamical cluster approximation to demonstrate the existence of a strange metal phase in three dimensions

Meshless methods for shear-deformable beams and plates based on mixed weak forms

Thin structural theories such as the shear-deformable Timoshenko beam and Reissner-Mindlin plate theories have seen wide use throughout engineering practice to simulate the response of structures with planar dimensions far larger than their thickness dimension. Meshless methods have been applied to construct numerical methods to solve the shear deformable theories. Similarly to the finite element method, meshless methods must be carefully designed to overcome the well-known shear-locking problem. Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed weak form. In the mixed weak form the shear stresses are treated as an independent variational quantity in addition to the usual displacement variables. We introduce a novel hybrid meshless-finite element formulation for the Timoshenko beam problem that converges to the stable first-order/zero-order finite element method in the local limit when using maximum entropy meshless basis functions. The resulting formulation is free from the effects shear-locking. We then consider the Reissner-Mindlin plate problem. The shear stresses can be identified as a vector field belonging to the Sobelov space with square integrable rotation, suggesting the use of rotated Raviart-Thomas-Nedelec elements of lowest-order for discretising the shear stress field. This novel formulation is again free from the effects of shear-locking. Finally we consider the construction of a generalised displacement method where the shear stresses are eliminated prior to the solution of the final linear system of equations. We implement an existing technique in the literature for the Stokes problem called the nodal volume averaging technique. To ensure stability we split the shear energy between a part calculated using the displacement variables and the mixed variables resulting in a stabilised weak form. The method then satisfies the stability conditions resulting in a formulation that is free from the effects of shear-locking.Open Acces

Modelling and numerical simulation of combustion and multi-phase flows using finite volume methods on unstructured meshes

The present thesis is devoted to the development and implementation of mathematical models and numerical methods in order to carry out computational simulations of complex heat and mass transfer phenomena. Several areas and topics in the field of Computational Fluid Dynamics (CFD) have been treated and covered during the development of the current thesis, specially combustion and dispersed multi-phase flows. This type of simulations requires the implementation and coupling of different physics. The numerical simulation of multiphysics phenomena is challenging due to the wide range of spatial and temporal scales which can characterize each one of the physics involved in the problem. Moreover, when solving turbulent flows, turbulence itself is a very complex physical phenomenon that can demand a huge computational effort. Hence, in order to make turbulent flow simulations computationally affordable, the turbulence should be modelled. Therefore, throughout this thesis different numerical methods and algorithms have been developed and implemented aiming to perform multiphysics simulations in turbulent flows. The first topic addressed is turbulent combustion. Chapter 2 presents a combustion model able to notably reduce the computational cost of the simulation. The model, namely the Progress-Variable (PV) model, relies on a separation of the spatio-temporal scales between the flow and the chemistry. Moreover, in order to account for the influence of the sub-grid species concentrations and energy fluctuations, the PV model is coupled to the Presumed Conditional Moment (PCM) model. Chapter 2 also shows the development of a smart load-balancing method for the evaluation of chemical reaction rates in parallel combustion simulations. Chapter 3 is devoted to dispersed multiphase flows. This type of flows are composed of a continuous phase and a dispersed phase in the form of unconnected particles or droplets. In this thesis, the Eulergian-Lagrangian approach has been selected. This type of model is the best-suited for dispersed multiphase flows with thousands or millions of particles, and with a flow regime ranging from the very dilute up to relatively dense. In Chapter 4, a new method capable of performing parallel numerical simulations using non-overlapping disconnected mesh domains with adjacent boundaries is presented. The presented algorithm stitches at each iteration independent meshes and solves them as a unique domain. Finally, Chapter 5 addresses a transversal aspect to the previously covered topics throughout the thesis. In this chapter, a self-adaptive strategy for the maximisation of the time-step for the numerical solution of convection-diffusion equations is discussed. The method is capable of determining dynamically at each iteration which is the maximum allowable time-step which assures a stable time integration. Moreover, the method also smartly modifies the temporal integration scheme in order to maximize its stability region depending on the properties of the system matrix.La present tesis està dedicada al desenvolupament e implementació de models matemàtics i mètodes numèrics amb l’objectiu de realitzar simulacions computacionals de fenòmens complexos de transferència de calor i massa. Diverses àrees i temes en el camp de la Dinàmica de Fluids Computacional (CFD) han sigut tractats i coberts durant el desenvolupament de la present tesi, en especial, la combustió i els fluxos multi-fase dispersos. Aquest tipus de simulacions de fenòmens multi-físics es desafiant degut al gran rang d’escales espaio-temporals que poden caracteritzar cada una de les físiques involucrades en el problema. D’altra banda, quan es resolen fluxos turbulents, la pròpia turbulència ja és un fenomen físic molt complex que pot requerir un gran esforç computacional. Per tant, amb l’objectiu de fer les simulacions computacionals de fluxos turbulents computacionalment assequibles, la turbulència ha de ser modelada. Per tant, durant aquesta tesis diferents mètodes i algoritmes han sigut desenvolupats e implementats amb l’objectiu de realitzar simulacions multi-físiques en fluxos turbulents. El primer tema abordat és la combustió turbulenta. El Capítol 2 presenta un model de combustió capaç de reduir notablement el cost computacional de la simulació. El model, anomenat el model Progress-Variable (PV), està basat en la separació d’escales espaio-temporals entre el fluid i la química. A més, amb l’objectiu de tenir en compte l’influencia de les fluctuacions a nivell sub-grid d’energia i concentracions d'espècies, el model PV s’acobla amb el model Presumed Conditional Moment (PCM). El Capítol 2 també mostra el desenvolupament d’un mètode intel·ligent de balanceig de càrrega per l'avaluació de el rati de reacció químic en simulacions de combustió paral·leles. El Capítol 3 està dedicat als fluxos multi-fase dispersos. Aquest tipus de fluids estan formats per una fase continua i una fase dispersa en forma de partícules o gotes inconnexes. En aquesta tesis, l’aproximació Euleriana-Lagrangiana ha sigut la seleccionada. Aquest tipus de model és el més adequat per fluxos multi-fase dispersos amb milers o milions de partícules, i amb règims que van des del molt diluït fins al relativament dens. Al Capítol 4, es presenta un nou mètode capaç de realitzar simulacions numèriques paral·leles utilitzant malles inconnexes no solapades que tenen fronteres adjacents. L’algoritme presentat cus a cada iteració les malles independents i les resol com un únic domini. Finalment, el Capítol 5 tracta un aspecte transversal a tots els temes coberts al llarg de la tesi. En aquest capítol es discuteix una estratègia auto-adaptativa destinada a la maximització del pas de temps per a la solució numèrica d’equacions de convecció-difusió. El mètode es capaç de determinar dinàmicament a cada iteració quin és el màxim pas de temps possible que assegura una integració temporal estable. A més, el mètode també modifica de forma intel·ligent la regió d’estabilitat en funció de les propietats de la matriu del sistema.Postprint (published version