Stability of nonlinear elliptic systems with distributed parameters and variable boundary data

AbstractIn this paper nonlinear partial differential equations of the elliptic type with the Dirichlet boundary data are investigated. Some sufficient conditions under which the solutions of considered equations depend continuously on parameters and boundary conditions are proved. The proofs of main results are based on variational methods. In the final part of the paper we give a short survey of the results and methods related to the question of stability of the boundary value problems

Multi-Pulse Laser Wakefield Acceleration: A New Route to Efficient, High-Repetition-Rate Plasma Accelerators and High Flux Radiation Sources

Laser-driven plasma accelerators can generate accelerating gradients three orders of magnitude larger than radio-frequency accelerators and have achieved beam energies above 1 GeV in centimetre long stages. However, the pulse repetition rate and wall-plug efficiency of plasma accelerators is limited by the driving laser to less than approximately 1 Hz and 0.1% respectively. Here we investigate the prospects for exciting the plasma wave with trains of low-energy laser pulses rather than a single high-energy pulse. Resonantly exciting the wakefield in this way would enable the use of different technologies, such as fibre or thin-disc lasers, which are able to operate at multi-kilohertz pulse repetition rates and with wall-plug efficiencies two orders of magnitude higher than current laser systems. We outline the parameters of efficient, GeV-scale, 10-kHz plasma accelerators and show that they could drive compact X-ray sources with average photon fluxes comparable to those of third-generation light source but with significantly improved temporal resolution. Likewise FEL operation could be driven with comparable peak power but with significantly larger repetition rates than extant FELs

A mesoscopic ring as a XNOR gate: An exact result

We describe XNOR gate response in a mesoscopic ring threaded by a magnetic flux $\phi$. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied in one arm of the ring which are treated as the inputs of the XNOR gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrode coupling strength, magnetic flux and gate voltages. Our theoretical study shows that, for a particular value of $\phi$ ($=\phi_0/2$) ($\phi_0=ch/e$, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the two inputs to the gate are the same, while if one but not both inputs are high (1), a low output current (0) results. It clearly exhibits the XNOR gate behavior and this aspect may be utilized in designing an electronic logic gate.Comment: 8 pages, 5 figure

Laserwire at the Accelerator Test Facility 2 with Sub-Micrometre Resolution

A laserwire transverse electron beam size measurement system has been developed and operated at the Accelerator Test Facility 2 (ATF2) at KEK. Special electron beam optics were developed to create an approximately 1 x 100 {\mu}m (vertical x horizontal) electron beam at the laserwire location, which was profiled using a 150 mJ, 71 ps laser pulse with a wavelength of 532 nm. The precise characterisation of the laser propagation allows the non-Gaussian transverse profiles of the electron beam caused by the laser divergence to be deconvolved. A minimum vertical electron beam size of 1.07 ${\pm}$ 0.06 (stat.) ${\pm}$ 0.05 (sys.) {\mu}m was measured. A vertically focussing quadrupole just before the laserwire was varied whilst making laserwire measurements and the projected vertical emittance was measured to be 82.56 ${\pm}$ 3.04 pm rad.Comment: 17 pages, 26 figures, submitted to Phys. Rev. ST Accel. Beam

Control of quantum interference in molecular junctions: Understanding the origin of Fano and anti- resonances

We investigate within a coarse-grained model the conditions leading to the appearance of Fano resonances or anti-resonances in the conductance spectrum of a generic molecular junction with a side group (T-junction). By introducing a simple graphical representation (parabolic diagram), we can easily visualize the relation between the different electronic parameters determining the regimes where Fano resonances or anti-resonances in the low-energy conductance spectrum can be expected. The results obtained within the coarse-grained model are validated using density-functional based quantum transport calculations in realistic T-shaped molecular junctions.Comment: 5 pages, 5 figure

A non-autonomous stochastic discrete time system with uniform disturbances

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family

Ubiquitin ligases and beyond

First paragraph (this article has no abstract): In a review published in 2004 [1] and that still repays reading today, Cecile Pickart traced the evolution of research on ubiquitination from its origins in the proteasomal degradation of proteins through the revelation that it has a central role in cell cycle regulation and the recognition of regulatory roles for ubiquitin in intracellular membrane transport, cell signalling, transcription, translation, and DNA repair

Constructing explicit magnetic analogies for the dynamics of glass forming liquids

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy