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The potentialities of double-drift region (DDR) impact avalanche transit time (IMPATT) devices based on group III–V semiconductor material Wurtzite-gallium nitride (Wz-GaN) as possible millimetre-wave (mm-wave) and terahertz (THz) sources have been explored in this paper. A large-signal (L-S) simulation technique based on a non-sinusoidal voltage excitation model (NVSE) developed by the authors has been used to study the high-frequency properties of DDR Wz-GaN IMPATTs at both mm-wave and THz frequencies. Similar studies have also been carried out for DDR IMPATTs based on some other conventional semiconductor materials such as GaAs (group III–V), InP (group III–V) and Si (group IV). Results show that DDR Wz-GaN IMPATTs excel all other devices under consideration as regards radio-frequency performance at both mm-wave and THz frequencies.

The external matter stress-tensor supporting charged Vaidya solution appears to violate weak energy condition in certain region of the spacetime. Motivated by this, a new interpretation of charged Vaidya solution was proposed by Ori [1] in which the energy condition continues to be satisfied. In this construction, one glues an outgoing Vaidya solution to the original ingoing Vaidya solution provided the surface where the external stress-tensor vanishes is spacelike. We revisit this study and extend it to higher-dimensions, to AdS settings, and to higher-derivative f(R) theories. In asymptotically flat space context, we explore in detail the case when the mass function m(v) is proportional to the charge function q(v). When the proportionality constant \nu = q(v)/m(v) lies in between zero and one, we show that the surface where the external stress-tensor vanishes is spacelike and lies in between the inner and outer apparent horizons., Comment: 21 pages; 1 LaTeX figure; v2 refs added, journal version

The use of different mathematical tools to study biological processes is necessary to capture effects occurring at different scales. Here we study as an example the immune response to infection with the bacteria Mycobacterium tuberculosis, the causative agent of tuberculosis (TB). Immune responses are both global (lymph nodes, blood, and spleen) as well as local (site of infection) in nature. Interestingly, the immune response in TB at the site of infection results in the formation of spherical structures comprised of cells, bacteria, and effector molecules known as granulomas. In this work, we use four different mathematical tools to explore both the global immune response as well as the more local one (granuloma formation) and compare and contrast results obtained using these methods. Applying a range of approaches from continuous deterministic models to discrete stochastic ones allows us to make predictions and suggest hypotheses about the underlying biology that might otherwise go unnoticed. The tools developed and applied here are also applicable in other settings such as tumor modeling.

Infection with Mycobacterium tuberculosis is a major world health problem. An estimated 2 billion people are presently infected and the disease causes approximately 3 million deaths per year. After bacteria are inhaled into the lung, a complex immune response is triggered leading to the formation of multicellular structures termed granulomas. It is believed that the collection of host granulomas either contain bacteria resulting in a latent infection or are unable to do so, leading to active disease. Thus, understanding granuloma formation and function is essential for improving both diagnosis and treatment of tuberculosis. Granuloma formation is a complex spatio-temporal system involving interactions of bacteria, specific immune cells, including macrophages, CD4+ and CD8+ T cells, as well as immune effectors such as chemokine and cytokines. To study this complex dynamical system we have developed an agent-based model of granuloma formation in the lung. This model combines continuous representations of chemokines with discrete agent representations of macrophages and T cells in a cellular automata-like environment. Our results indicate that key host elements involved in granuloma formation are chemokine diffusion, prevention of macrophage overcrowding within the granuloma, arrival time, location and number of T cells within the granuloma, and an overall host ability to activate macrophages. Interestingly, a key bacterial factor is its intracellular growth rate, whereby slow growth actually facilitates survival.

We initiate the study of computable model theory of modal logic, by proving effective completeness theorems for a variety of first-order modal logics. We formulate a natural definition of a decidable Kripke model, and show how to construct such a decidable Kripke model of a given decidable theory. Our construction is inspired by the effective Henkin construction for classical logic. The Henkin construction, however, depends in an essential way on the Deduction Theorem. In its usual form the Deduction Theorem fails for modal logic. In our construction, the Deduction Theorem is replaced by a result about objects called finite Kripke diagrams. We argue that this result can be viewed as an analogue of the Deduction Theorem for modal logic.

We find a regime in which a strongly coupled striped superconductor features a superconducting dome. This regime is signified by i) a modulating chemical potential that averages to zero, and ii) a superconducting order parameter that has a scaling dimension larger than 3/2 but less than or equal to 3. We also find that in this regime, the order parameter exhibits a mild dependence on the modulation wavelength of the stripe., 5 pages, 4 figures

We study the interplay between the stripe order and the superconducting order in a strongly coupled striped superconductor using gauge/gravity duality. In particular, we study the effects of inhomogeneity introduced by the stripe order on the superconducting transition temperature beyond the mean field level by including the effects of backreaction onto the spacetime geometry in the dual gravitational picture. We find that inhomogeneity \emph{enhances} the critical temperature relative to its value for the uniform system., 8 pages, 7 figures

Let \(Mf(x) = \sup(1/2r)\int^{x+r}_{x-r} |f(t)|\;dt\) be the centered maximal operator on the line. Through a numerical search procedure, we have conjectural best constants for the weak-type 1-1 estimate (3/2) and the Lp estimate (the constant B(p,1) such that \(M(|x|^{-1/p}) = B(p,1)|x|^{-1/p}).\) We prove that these constants are lower bounds for the best constants and discuss the numerical evidence for the conjectures.

We analytically calculate properties of a strongly coupled striped superconductor, with the charge density wave sourced by a modulated chemical potential, in the large modulation wavenumber Q limit. In the absence of a homogeneous term in the chemical potential, we show that the critical temperature scales as a negative power of Q for scaling dimensions \Delta < 3/2, whereas for \Delta > 3/2, there is no phase transition above a certain critical value of Q. The condensate is found to scale as a positive power of Q such that the gap is proportional to Q. We discuss how these results change if a homogeneous term is added to the chemical potential. We compare our analytic results with numerical calculations whenever the latter are available and find good agreement., Comment: 24 pages, 6 figures; published version: low T behavior and discussion added

The immune response to Mycobacterium tuberculosis infection (Mtb) is the formation of unique lesions, called granulomas. How well these granulomas form and function is a key issue that might explain why individuals experience different disease outcomes. The spatial structures of these granulomas are not well understood. In this paper, we use a metapopulation framework to develop a spatio-temporal model of the immune response to Mtb. Using this model, we are able to investigate the spatial organization of the immune response in the lungs to Mtb. We identify both host and pathogen factors that contribute to successful infection control. Additionally, we identify specific spatial interactions and mechanisms important for successful granuloma formation. These results can be further studied in the experimental setting.

In this work we re-examine an existing model of gastric acid secretion. The model is a 2-compartment model of the human stomach accounting for regions where relevant cells (D, G, ECL and parietal cells) and proteins and acid they secrete (somatostatin, gastrin, histamine, and gastric acid, respectively) are found. These proteins compose a positive and negative feedback system that controls the secretion of gastric acid by parietal cells. The original model consists of 18 ordinary differential equations and yields a stable 3-period limit cycle solution. We modify the existing model by introducing a delay into the system and assuming that the cell populations are in steady state over a short-time window (

Large-signal (L-S) characterizations of double-drift region (DDR) impact avalanche transit time (IMPATT) devices based on group III–V semiconductors such as wurtzite (Wz) GaN, GaAs and InP have been carried out at both millimeter-wave (mm-wave) and terahertz (THz) frequency bands. A L-S simulation technique based on a non-sinusoidal voltage excitation (NSVE) model developed by the authors has been used to obtain the high frequency properties of the above mentioned devices. The effect of band-to-band tunneling on the L-S properties of the device at different mm-wave and THz frequencies are also investigated. Similar studies are also carried out for DDR IMPATTs based on the most popular semiconductor material, i.e. Si, for the sake of comparison. A comparative study of the devices based on conventional semiconductor materials (i.e. GaAs, InP and Si) with those based on Wz-GaN shows significantly better performance capabilities of the latter at both mm-wave and THz frequencies.