Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Current-Controlled Negative Differential Resistance due to Joule Heating in TiO2

We show that Joule heating causes current-controlled negative differential resistance (CC-NDR) in TiO2 by constructing an analytical model of the voltage-current V(I) characteristic based on polaronic transport for Ohm's Law and Newton's Law of Cooling, and fitting this model to experimental data. This threshold switching is the 'soft breakdown' observed during electroforming of TiO2 and other transition-metal-oxide based memristors, as well as a precursor to 'ON' or 'SET' switching of unipolar memristors from their high to their low resistance states. The shape of the V(I) curve is a sensitive indicator of the nature of the polaronic conduction.Comment: 13 pages, 2 figure

From nothing to something: discrete integrable systems

Chinese ancient sage Laozi said that everything comes from `nothing'. Einstein believes the principle of nature is simple. Quantum physics proves that the world is discrete. And computer science takes continuous systems as discrete ones. This report is devoted to deriving a number of discrete models, including well-known integrable systems such as the KdV, KP, Toda, BKP, CKP, and special Viallet equations, from `nothing' via simple principles. It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra, model-independent nonlinear superpositions of a trivial integrable system (Riccati equation), index homogeneous decompositions of the simplest geometric theorem (the angle bisector theorem), as well as the M\"obious transformation invariants.Comment: 11 pages, side 10 repor

Cell-Type Specific Changes in Glial Morphology and Glucocorticoid Expression During Stress and Aging in the Medial Prefrontal Cortex.

Repeated exposure to stressors is known to produce large-scale remodeling of neurons within the prefrontal cortex (PFC). Recent work suggests stress-related forms of structural plasticity can interact with aging to drive distinct patterns of pyramidal cell morphological changes. However, little is known about how other cellular components within PFC might be affected by these challenges. Here, we examined the effects of stress exposure and aging on medial prefrontal cortical glial subpopulations. Interestingly, we found no changes in glial morphology with stress exposure but a profound morphological change with aging. Furthermore, we found an upregulation of non-nuclear glucocorticoid receptors (GR) with aging, while nuclear levels remained largely unaffected. Both changes are selective for microglia, with no stress or aging effect found in astrocytes. Lastly, we show that the changes found within microglia inversely correlated with the density of dendritic spines on layer III pyramidal cells. These findings suggest microglia play a selective role in synaptic health within the aging brain

λϕ4\lambda\phi^4 model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($\mu_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($\mu_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $\mu_c\approx 0.547\times 10^{15}$GeV and $\mu_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.Comment: 12 pages, LaTex, no figur