Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations

We study characteristic Cauchy problems for the Korteweg-deVries (KdV) equation $u_t=uu_x+u_{xxx}$, and the Kadomtsev-Petviashvili (KP) equation $u_{yy}=\bigl(u_{xxx}+uu_x+u_t\bigr)_x$ with holomorphic initial data possessing nonnegative Taylor coefficients around the origin. For the KdV equation with initial value $u(0,x)=u_0(x)$, we show that there is no solution holomorphic in any neighbourhood of $(t,x)=(0,0)$ in ${\mathbb C}^2$ unless $u_0(x)=a_0+a_1x$. This also furnishes a nonexistence result for a class of $y$-independent solutions of the KP equation. We extend this to $y$-dependent cases by considering initial values given at $y=0$, $u(t,x,0)=u_0(x,t)$, $u_y(t,x,0)=u_1(x,t)$, where the Taylor coefficients of $u_0$ and $u_1$ around $t=0$, $x=0$ are assumed nonnegative. We prove that there is no holomorphic solution around the origin in ${\mathbb C}^3$ unless $u_0$ and $u_1$ are polynomials of degree 2 or lower.Comment: 17 pages in LaTeX2e, to appear in Stud. Appl. Mat

Study of techniques for the reduction of creep in plated wire memories Final report, 28 Jun. 1967 - 28 Aug. 1968

Magnetization reversal in thin films of plated wire memory element

Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures with Free Body Motion

Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. The stability conditions in this paper are given purely in terms of properties of the plant and controller transfer function matrices, although the proofs rely on state space techniques. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented

Estimation of the shear viscosity at finite net-baryon density from A+A collision data at sNN=7.7−200\sqrt{s_\mathrm{NN}} = 7.7-200 GeV

Hybrid approaches based on relativistic hydrodynamics and transport theory have been successfully applied for many years for the dynamical description of heavy ion collisions at ultrarelativistic energies. In this work a new viscous hybrid model employing the hadron transport approach UrQMD for the early and late non-equilibrium stages of the reaction, and 3+1 dimensional viscous hydrodynamics for the hot and dense quark-gluon plasma stage is introduced. This approach includes the equation of motion for finite baryon number, and employs an equation of state with finite net-baryon density to allow for calculations in a large range of beam energies. The parameter space of the model is explored, and constrained by comparison with the experimental data for bulk observables from SPS and the phase I beam energy scan at RHIC. The favored parameter values depend on energy, but allow to extract the effective value of the shear viscosity coefficient over entropy density ratio $\eta/s$ in the fluid phase for the whole energy region under investigation. The estimated value of $\eta/s$ increases with decreasing collision energy, which may indicate that $\eta/s$ of the quark-gluon plasma depends on baryochemical potential $\mu_B$.Comment: minor changes in the text, results for constant eta*T/w added. Version accepted for publication in Phys. Rev.

Cell migration on material-driven fibronectin microenvironments

Cell migration is a fundamental process involved in a wide range of biological phenomena. However, how the underlying mechanisms that control migration are orchestrated is not fully understood. In this work, we explore the migratory characteristics of human fibroblasts using different organisations of fibronectin (FN) triggered by two chemically similar surfaces, poly(ethyl acrylate) (PEA) and poly(methyl acrylate) (PMA); cell migration is mediated via an intermediate layer of fibronectin (FN). FN is organised into nanonetworks upon simple adsorption on PEA whereas a globular conformation is observed on PMA. We studied cell speed over the course of 24 h and the morphology of focal adhesions in terms of area and length. Additionally, we analysed the amount of cell-secreted FN as well as FN remodelling. Velocity of human fibroblasts was found to exhibit a biphasic behaviour on PEA, whereas it remained fairly constant on PMA. FA analysis revealed more mature focal adhesions on PEA over time contrary to smaller FAs found on PMA. Finally, human fibroblasts seemed to remodel adsorbed FN more on PMA than on PEA. Overall, these results indicate that the cell–protein–material interface affects cell migratory behaviour. Analysis of FAs together with FN secretion and remodelling were associated with differences in cell velocity providing insights into the factors that can modulate cell motility

Aberrations in shift-invariant linear optical imaging systems using partially coherent fields

Here the role and influence of aberrations in optical imaging systems employing partially coherent complex scalar fields is studied. Imaging systems require aberrations to yield contrast in the output image. For linear shift-invariant optical systems, we develop an expression for the output cross-spectral density under the space-frequency formulation of statistically stationary partially coherentfields. We also develop expressions for the output cross{spectral density and associated spectral density for weak-phase, weak-phase-amplitude, and single-material objects in one transverse spatial dimension