Influence of realistic parameters on state-of-the-art LWFA experiments

We examine the influence of non-ideal plasma-density and non-Gaussian transverse laser-intensity profiles in the laser wakefield accelerator analytically and numerically. We find that the characteristic amplitude and scale length of longitudinal density fluctuations impacts on the final energies achieved by electron bunches. Conditions that minimize the role of the longitudinal plasma density fluctuations are found. The influence of higher order Laguerre-Gaussian laser pulses is also investigated. We find that higher order laser modes typically lead to lower energy gains. Certain combinations of higher order modes may, however, lead to higher electron energy gains.Comment: 16 pages, 6 figures; Accepted for publication in Plasma Physics and Controlled Fusio

Exposing errors related to weak memory in GPU applications

© 2016 ACM.We present the systematic design of a testing environment that uses stressing and fuzzing to reveal errors in GPU applications that arise due to weak memory effects. We evaluate our approach on seven GPUS spanning three NVIDIA architectures, across ten CUDA applications that use fine-grained concurrency. Our results show that applications that rarely or never exhibit errors related to weak memory when executed natively can readily exhibit these errors when executed in our testing environment. Our testing environment also provides a means to help identify the root causes of such errors, and automatically suggests how to insert fences that harden an application against weak memory bugs. To understand the cost of GPU fences, we benchmark applications with fences provided by the hardening strategy as well as a more conservative, sound fencing strategy

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

Suppression of core polarization in halo nuclei

We present a microscopic study of halo nuclei, starting from the Paris and Bonn potentials and employing a two-frequency shell model approach. It is found that the core-polarization effect is dramatically suppressed in such nuclei. Consequently the effective interaction for halo nucleons is almost entirely given by the bare G-matrix alone, which presently can be evaluated with a high degree of accuracy. The experimental pairing energies between the two halo neutrons in $^6$He and $^{11}$Li nuclei are satisfactorily reproduced by our calculation. It is suggested that the fundamental nucleon-nucleon interaction can be probed in a clearer and more direct way in halo nuclei than in ordinary nuclei.Comment: 11 pages, RevTex, 2 postscript figures; major revisions, matches version to appear in Phys. Rev. Letter

Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle

Closed-form expressions are obtained for the partition function of the Ising model on an M x N simple-quartic lattice embedded on a Moebius strip and a Klein bottle for finite M and N. The finite-size effects at criticality are analyzed and compared with those under cylindrical and toroidal boundary conditions. Our analysis confirms that the central charge is c=1/2.Comment: 8 pages, 3 eps figure

Spanning Trees on Graphs and Lattices in d Dimensions

The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees $N_{ST}$ and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in $d\geq 2$ dimensions, and is applied to the hypercubic, body-centered cubic, face-centered cubic, and specific planar lattices including the kagom\'e, diced, 4-8-8 (bathroom-tile), Union Jack, and 3-12-12 lattices. This leads to closed-form expressions for $N_{ST}$ for these lattices of finite sizes. We prove a theorem concerning the classes of graphs and lattices ${\cal L}$ with the property that $N_{ST} \sim \exp(nz_{\cal L})$ as the number of vertices $n \to \infty$, where $z_{\cal L}$ is a finite nonzero constant. This includes the bulk limit of lattices in any spatial dimension, and also sections of lattices whose lengths in some dimensions go to infinity while others are finite. We evaluate $z_{\cal L}$ exactly for the lattices we considered, and discuss the dependence of $z_{\cal L}$ on d and the lattice coordination number. We also establish a relation connecting $z_{\cal L}$ to the free energy of the critical Ising model for planar lattices ${\cal L}$.Comment: 28 pages, latex, 1 postscript figure, J. Phys. A, in pres

Spanning trees on the Sierpinski gasket

We obtain the numbers of spanning trees on the Sierpinski gasket $SG_d(n)$ with dimension $d$ equal to two, three and four. The general expression for the number of spanning trees on $SG_d(n)$ with arbitrary $d$ is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are also obtained.Comment: 20 pages, 8 figures, 1 tabl

Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links

We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in task-completion networks, and gradient driven transport on networks. Changing the parameters of the distance-dependence, we found a rich phase diagram, with different transient and recurrent phases in the context of random walks on networks. We performed the calculations in two limiting cases: in the annealed case, where the rearrangement of the random links is fast, and in the quenched case, where the link rearrangement is slow compared to the motion of the random walker or the surface. It has been well-established that in a large class of interacting systems, adding an arbitrarily small density of, possibly long-range, quenched random links to a regular lattice interaction topology, will give rise to mean-field (or annealed) like behavior. In some cases, however, mean-field scaling breaks down, such as in diffusion or in the Edwards-Wilkinson process in "low-dimensional" small-world networks. This break-down can be understood by treating the random links perturbatively, where the mean-field (or annealed) prediction appears as the lowest-order term of a naive perturbation expansion. The asymptotic analytic results are also confirmed numerically by employing exact numerical diagonalization of the network Laplacian. Further, we construct a finite-size scaling framework for the relevant observables, capturing the cross-over behaviors in finite networks. This work provides a detailed account of the self-consistent-perturbative and renormalization approaches briefly introduced in two earlier short reports.Comment: 36 pages, 27 figures. Minor revisions in response to the referee's comments. Furthermore, some typos were fixed and new references were adde

Angular Dependences of Third Harmonic Generation from Microdroplets

We present experimental and theoretical results for the angular dependence of third harmonic generation (THG) of water droplets in the micrometer range (size parameter $62<ka<248$). The THG signal in $p$- and $s$-polarization obtained with ultrashort laser pulses is compared with a recently developed nonlinear extension of classical Mie theory including multipoles of order $l\leq250$. Both theory and experiment yield over a wide range of size parameters remarkably stable intensity maxima close to the forward and backward direction at ``magic angles''. In contrast to linear Mie scattering, both are of comparable intensity.Comment: 4 pages, RevTeX, 3 figures available on request from [email protected], submitted to PR