Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation

We present a method for solving the linearized Vlasov-Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior

Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100 terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, three-dimensional particle-in-cell modelling are examined. First, the Cartesian code VORPAL using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code CALDER-CIRC uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of the two simulations indicates that they are free of numerical artefacts. Both approaches thus retrieve physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver

An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

Effective Hamiltonian approach to adiabatic approximation in open systems

The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation are established and discussed. A High-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin-$\frac 1 2$ particle in time-dependent magnetic fields is analyzed.Comment: 6 pages, 2 figure

Sea-ice microbial communities in the Central Arctic Ocean: Limited responses to short-term pCO(2) perturbations

The Arctic Ocean is more susceptible to ocean acidification than other marine environments due to its weaker buffering capacity, while its cold surface water with relatively low salinity promotes atmospheric CO 2 uptake. We studied how sea-ice microbial communities in the central Arctic Ocean may be affected by changes in the carbonate system expected as a consequence of ocean acidification. In a series of four experiments during late summer 2018 aboard the icebreaker Oden, we addressed microbial growth, production of dissolved organic carbon (DOC) and extra- cellular polymeric substances (EPS), photosynthetic activity, and bacterial assemblage structure as sea-ice microbial communities were exposed to elevated partial pressures of CO 2 (pCO 2 ). We incubated intact, bottom ice-core sections and dislodged, under-ice algal aggregates (dominated by Melosira arctica) in separate experiments under approximately 400, 650, 1000, and 2000 micro atm pCO 2 for 10 d under different nutrient regimes. The results indicate that the growth of sea-ice algae and bacteria was unaffected by these higher pCO 2 levels, and concentrations of DOC and EPS were unaffected by a shifted inorganic C/N balance, resulting from the CO 2 enrichment. These central Arctic sea-ice microbial communities thus appear to be largely insensitive to short-term pCO 2 perturbations. Given the natural, seasonally driven fluctuations in the carbonate system of sea ice, its resident microorganisms may be sufficiently tolerant of large variations in pCO 2 and thus less vulnerable than pelagic communities to the impacts of ocean acidification, increasing the ecological importance of sea-ice microorganisms even as the loss of Arctic sea ice continue

Software to compute infinitesimal symmetries of exterior differenial systems, with applications

A description is given of a software package to compute symmetries of partial differential equations, using computer algebra. As an application, the computation of higher-order symmetries of the classical Boussinesq equation is given leading to the recursion operator for symmetries in a straightforward way. Nonlocal symmetries for the Federbush model are obtained yielding the linearization of the model

Implementation of a method to visualize noise-induced hearing loss in mass stranded cetaceans

Assessment of the impact of noise over-exposure in stranded cetaceans is challenging, as the lesions that lead to hearing loss occur at the cellular level and inner ear cells are very sensitive to autolysis. Distinguishing ante-mortem pathology from post-mortem change has been a major constraint in diagnosing potential impact. Here, we outline a methodology applicable to the detection of noise-induced hearing loss in stranded cetaceans. Inner ears from two mass strandings of long-finned pilot whales in Scotland were processed for scanning electron microscopy observation. In one case, a juvenile animal, whose ears were fixed within 4¿hours of death, revealed that many sensory cells at the apex of the cochlear spiral were missing. In this case, the absence of outer hair cells would be compatible with overexposure to underwater noise, affecting the region which transduces the lowest frequencies of the pilot whales hearing spectrum. Perfusion of cochlea with fixative greatly improved preservation and enabled diagnostic imaging of the organ of Corti, even 30¿hours after death. This finding supports adopting a routine protocol to detect the pathological legacy of noise overexposure in mass stranded cetaceans as a key to understanding the complex processes and implications that lie behind such stranding events

Surface Ocean pCO2 Seasonality and Sea-Air CO2 Flux Estimates for the North American East Coast

Underway and in situ observations of surface ocean pCO2, combined with satellite data, were used to develop pCO2 regional algorithms to analyze the seasonal and interannual variability of surface ocean pCO2 and sea-air CO2 flux for five physically and biologically distinct regions of the eastern North American continental shelf: the South Atlantic Bight (SAB), the Mid-Atlantic Bight (MAB), the Gulf of Maine (GoM), Nantucket Shoals and Georges Bank (NS+GB), and the Scotian Shelf (SS). Temperature and dissolved inorganic carbon variability are the most influential factors driving the seasonality of pCO2. Estimates of the sea-air CO2 flux were derived from the available pCO2 data, as well as from the pCO2 reconstructed by the algorithm. Two different gas exchange parameterizations were used. The SS, GB+NS, MAB, and SAB regions are net sinks of atmospheric CO2 while the GoM is a weak source. The estimates vary depending on the use of surface ocean pCO2 from the data or algorithm, as well as with the use of the two different gas exchange parameterizations. Most of the regional estimates are in general agreement with previous studies when the range of uncertainty and interannual variability are taken into account. According to the algorithm, the average annual uptake of atmospheric CO2 by eastern North American continental shelf waters is found to be between 3.4 and 5.4 Tg C/yr (areal average of 0.7 to 1.0 mol CO2 /sq m/yr) over the period 2003-2010

On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure