Current issues in finite-TT density-functional theory and Warm-Correlated Matter

Finite-temperature DFT has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM). Subclasses of WCM are Warm-dense matter (WDM), ultra-fast matter (UFM), and high-energy density matter (HEDM), containing electyrons (e) and ions (i). Strong e-e, i-i and e-i correlation effects and partial degeneracies are found in these systems where the electron temperature $T_e$ is comparable to the electron Fermi energy. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge $Z_j$. Quasi-equilibria with the ion temperature $T_i\ne T_e$ are common. The ion subsystem in WCM can no longer be treated as a passive "external potential", as is customary in $T=0$ density functional theory (DFT) dominated by solid-state theory or quantum chemistry. Hohenberg-Kohn-Mermin theory can be used for WCMs if finite-$T$ exchange-correlation (XC) functionals are available. They are functionals of both the one-body electron density $n_e$ and the one-body ion densities $\rho_j$. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated {\it in situ}, directly from the pair-distribution functions. This eliminates the need for any XC-functionals, or the use of a Born-Oppenheimer approximation. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-$T$ XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review current developments and concerns in finite-$T$ DFT, especially in the context of non-relativistic warm-dense matter and ultra-fast matter will be presented.Comment: Presented at the DFT16 meeting in Debrecen, Hungary, September 2015, held on the 50th anniversary of Kohn-Sham Theory, 10 pages, 3 figure

Thermal Stability of Metallic Single-Walled Carbon Nanotubes: An O(N) Tight-Binding Molecular Dynamics Simulation Study

Order(N) Tight-Binding Molecular Dynamics (TBMD) simulations are performed to investigate the thermal stability of (10,10) metallic Single-Walled Carbon Nanotubes (SWCNT). Periodic boundary conditions (PBC) are applied in axial direction. Velocity Verlet algorithm along with the canonical ensemble molecular dynamics (NVT) is used to simulate the tubes at the targeted temperatures. The effects of slow and rapid temperature increases on the physical characteristics, structural stability and the energetics of the tube are investigated and compared. Simulations are carried out starting from room temperature and the temperature is raised in steps of 300K. Stability of the simulated metallic SWCNT is examined at each step before it is heated to higher temperatures. First indication of structural deformation is observed at 600K. For higher heat treatments the deformations are more pronounced and the bond breaking temperature is reached around 2500K. Gradual (slow) heating and thermal equilibrium (fast heating) methods give the value of radial thermal expansion coefficient in the temperature range between 300K-600K as 0.31x10^{-5}(1/K) and 0.089x10^{-5}(1/K), respectively. After 600K, both methods give the same value of 0.089x10^{-5}(1/K). The ratio of the total energy per atom with respect to temperature is found to be 3x10^{-4} eV/K

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: incandecence and luminescence in arbitrary geometries

We describe a fluctuating volume--current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume--integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associatedmatrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles

Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter

This paper investigates the state estimation of a high-fidelity spatially resolved thermal- electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1 % in less than 200 s despite a 30 % error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.Comment: Submitted to the Journal of Power Source

A Manufacturer Design Kit for Multi-Chip Power Module Layout Synthesis

The development of Multi-Chip Power Modules (MCPMs) has been a key factor in recent advancements in power electronics technologies. MCPMs achieve higher power density by combining multiple power semiconductor devices into one package. The work detailed in this thesis is part of an ongoing project to develop a computer-aided design software tool known as PowerSynth for MCPM layout synthesis and optimization. This thesis focuses on the definition and design of a Manufacturer Design Kit (MDK) for PowerSynth, which enables the designer to design an MCPM for a manufacturer’s fabrication process. The MDK is comprised of a layer stack and technology library, design rule checking (DRC), and layout versus schematic checking. File formats have been defined for layer stack and design rule input, and import functions have been written and integrated with the existing user interface and data structures to allow PowerSynth to accept these file formats as a form of input. Finally, an exhaustive DRC function has been implemented to allow the designer to verify that a synthesized layout meets all design rules before committing the design to manufacturing. This function was validated by running DRC on an example layout solution using two different sets of design rules