arXiv subjects

Stefan Weber

Publications and source records attributed to Stefan Weber.

35 records · Page 2Linked to original sources

arXiv2022

High-Order Curvilinear Finite Element Magneto-Hydrodynamics I: A Conservative Lagrangian Scheme

Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena. The classical Lagrangian methods are typically limited to the low orders of convergence and suffer from violation of the divergence-free condition for magnetic field or conservation of the invariants. This paper is the first part of a new series about high-order non-ideal magneto-hydrodynamics, where a multi-dimensional conservative Lagrangian method based on curvilinear finite elements is presented. The condition on zero divergence of magnetic field and conservation of mass, momentum, magnetic flux and the total energy are satisfied exactly. The curvilinear elements prevent entangling of the computational mesh and its imprinting into the solution. A high-order conservative time integration is applied, where an arbitrary order of convergence is attained for problems of ideal magneto-hydrodynamics. The resistive magnetic field diffusion is solved by an implicit scheme. Description of the method is given and multiple test problems demonstrating properties of the scheme are performed. The construction of the method and possible future directions of development are discussed.

physics.comp-ph↗

arXiv2022

Simulation Methods for Robust Risk Assessment and the Distorted Mix Approach

Uncertainty requires suitable techniques for risk assessment. Combining stochastic approximation and stochastic average approximation, we propose an efficient algorithm to compute the worst case average value at risk in the face of tail uncertainty. Dependence is modelled by the distorted mix method that flexibly assigns different copulas to different regions of multivariate distributions. We illustrate the application of our approach in the context of financial markets and cyber risk.

q-fin.RM↗

arXiv2021

Capital Requirements and Claims Recovery: A New Perspective on Solvency Regulation

Protection of creditors is a key objective of financial regulation. Where the protection needs are high, i.e., in banking and insurance, regulatory solvency requirements are an instrument to prevent that creditors incur losses on their claims. The current regulatory requirements based on Value at Risk and Average Value at Risk limit the probability of default of financial institutions, but they fail to control the size of recovery on creditors' claims in the case of default. We resolve this failure by developing a novel risk measure, Recovery Value at Risk. Our conceptual approach can flexibly be extended and allows the construction of general recovery risk measures for various risk management purposes. By design, these risk measures control recovery on creditors' claims and integrate the protection needs of creditors into the incentive structure of the management. We provide detailed case studies and applications: We analyze how recovery risk measures react to the joint distributions of assets and liabilities on firms' balance sheets and compare the corresponding capital requirements with the current regulatory benchmarks based on Value at Risk and Average Value at Risk. We discuss how to calibrate recovery risk measures to historic regulatory standards. Finally, we show that recovery risk measures can be applied to performance-based management of business divisions of firms and that they allow for a tractable characterization of optimal tradeoffs between risk and return in the context of investment management.

q-fin.RM↗

arXiv2021

Radiation induced acceleration of ions

Radiation friction can have a substantial impact on electron dynamics in a transparent target exposed to a strong laser pulse. In particular, by modifying quiver electron motion, it can strongly enhance the longitudinal charge separation field, thus stimulating ion acceleration. We present a model and simulation results for such a radiation induced ion acceleration and study the scalings of the maximal attainable and average ion energies with respect to the laser and target parameters. We also compare the performance of this mechanism to the conventional ones.

physics.plasm-ph↗

arXiv2021

Market Efficient Portfolios in a Systemic Economy

We study the ex-ante minimization of market inefficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of leverage targeting banks, which rebalance their portfolios in response to asset shocks. We characterize market inefficiency in terms of two key drivers, the banks' systemic significance and the statistical moments of asset shocks, and develop an explicit expression for the matrix of asset holdings which minimizes such inefficiency. Our analysis shows that to reduce inefficiencies, portfolio holdings should deviate more from a full diversification strategy if there is little heterogeneity in banks' systemic significance.

q-fin.RM↗

arXiv2020

Bremsstrahlung emission and plasma characterization driven by moderately relativistic laser-plasma interactions

Relativistic electrons generated by the interaction of petawatt-class short laser pulses with solid targets can be used to generate bright X-rays via bremsstrahlung. The efficiency of laser energy transfer into these electrons depends on multiple parameters including the focused intensity and pre-plasma level. This paper reports experimental results from the interaction of a high intensity petawatt-class glass laser pulses with solid targets at a maximum intensity of $10^{19}$ W/cm$^2$. In-situ measurements of specularly reflected light are used to provide an upper bound of laser absorption and to characterize focused laser intensity, the pre-plasma level and the generation mechanism of second harmonic light. The measured spectrum of electrons and bremsstrahlung radiation provide information about the efficiency of laser energy transfer.

physics.plasm-ph↗

arXiv2020

Absorption and opacity threshold for a thin foil in a strong circularly polarized laser field

We show that a commonly accepted transparency threshold for a thin foil in a strong circularly polarized normally incident laser pulse needs a refinement. We present a new analytical model, which correctly accounts for laser absorption. The refined threshold is determined not solely by the laser amplitude, but other parameters are equally or even more important. Our predictions are in a perfect agreement with PIC simulations. The refined criterion is crucial for configuring laser plasma experiments in the high field domain. Besides, an opaque foil steepens the pulse front, this can be important for numerous applications.

physics.plasm-ph↗

arXiv2019

Stochastic mortality models: An infinite dimensional approach

Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is the introduction of a family of processes called forward mortality improvements which provide a flexible tool for a simple construction of stochastic forward mortality models. In practice, the notion of mortality improvements are a convenient device for the quantification of changes in mortality rates over time that enables, for example, the detection of cohort effects. We show that the forward mortality rates satisfy Heath-Jarrow-Morton-type consistency conditions which translate to the forward mortality improvements. While the consistency conditions of the forward mortality rates are analogous to the classical conditions in the context of bond markets, the conditions of the forward mortality improvements possess a different structure: forward mortality models include a cohort parameter besides the time horizon; these two dimensions are coupled in the dynamics of consistent models of forwards mortality improvements. In order to obtain a unified framework, we transform the systems of Itô-processes which describe the forward mortality rates and improvements: in contrast to term-structure models, the corresponding stochastic partial differential equations (SPDEs) describe the random dynamics of two-dimensional surfaces rather than curves.

math.PR↗

arXiv2017

Solvency II, or How to Sweep the Downside Risk Under the Carpet

Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate networks, unless a consolidated solvency balance sheet is required for each economic scenario. In this case, they can largely reduce their total capital requirements via appropriate transfer agreements within a network structure consisting of sufficiently many entities and thereby circumvent capital regulation. We prove several versions of such a result for general distortion risk measures of V@R-type, explicitly construct suitable allocations of the network portfolio, and finally demonstrate how these findings can be extended beyond distortion risk measures. We also discuss why consolidation requirements cannot completely eliminate this problem. Capital regulation should thus be based on coherent or convex risk measures like average value at risk or expectiles.

q-fin.RM↗

arXiv2017

Multi-GeV electron-positron beam generation from laser-electron scattering

The new generation of laser facilities is expected to deliver short (10 fs - 100 fs) laser pulses with 10 - 100 PW of peak power. This opens an opportunity to study matter at extreme intensities in the laboratory and provides access to new physics. Here we propose to scatter GeV-class electron beams from laser-plasma accelerators with a multi-PW laser at normal incidence. In this configuration, one can both create and accelerate electron-positron pairs. The new particles are generated in the laser focus and gain relativistic momentum in the direction of laser propagation. Short focal length is an advantage, as it allows the particles to be ejected from the focal region with a net energy gain in vacuum. Electron-positron beams obtained in this setup have a low divergence, are quasi-neutral and spatially separated from the initial electron beam. The pairs attain multi-GeV energies which are not limited by the maximum energy of the initial electron beam. We present an analytical model for the expected energy cutoff, supported by 2D and 3D particle-in-cell simulations. The experimental implications, such as the sensitivity to temporal synchronisation and laser duration is assessed to provide guidance for the future experiments.

physics.plasm-ph↗

arXiv2017

Gravitational wave generation by interaction of high power lasers with matter using shock waves

Gravitational wave generation by a strong shock wave in the interaction of high power laser with matter is analyzed in linear approximation of gravitational theory. The analytical formulas and estimates are derived for the metric perturbations and the radiated power of the generated gravitational waves. Furthermore the characteristics of polarization and the behavior of test particles are investigated in the presence of gravitational wave which will be important for the detection.

gr-qc↗

arXiv2016

Measures of Systemic Risk

Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a novel approach to measuring systemic risk. Key to our construction is a rigorous derivation of systemic risk measures from the structure of the underlying system and the objectives of a financial regulator. The suggested systemic risk measures express systemic risk in terms of capital endowments of the financial firms. Their definition requires two ingredients: a cash flow or value model that assigns to the capital allocations of the entities in the system a relevant stochastic outcome; and an acceptability criterion, i.e. a set of random outcomes that are acceptable to a regulatory authority. Systemic risk is measured by the set of allocations of additional capital that lead to acceptable outcomes. We explain the conceptual framework and the definition of systemic risk measures, provide an algorithm for their computation, and illustrate their application in numerical case studies. Many systemic risk measures in the literature can be viewed as the minimal amount of capital that is needed to make the system acceptable after aggregating individual risks, hence quantify the costs of a bail-out. In contrast, our approach emphasizes operational systemic risk measures that include both ex post bailout costs as well as ex ante capital requirements and may be used to prevent systemic crises.

q-fin.RM↗

arXiv2016

Gravitational waves generated by laser accelerated relativistic ions

The generation of gravitational waves by laser accelerated relativistic ions is investigated. The piston and light sail models of laser plasma acceleration are considered and analytical expressions for space-time metric perturbation are derived. For both models the dependence of gravitational waves amplitude on the laser and plasma parameters as well as gravitational waves spectrum and angular distribution are examined

physics.plasm-ph↗

arXiv2016

Gravitational wave generation by interaction of high power lasers with matter. Part II: Ablation and Piston models

We analyze theoretical models of gravitational waves generation in the interaction of high intensity laser with matter, namely ablation and piston models. We analyse the generated gravitational waves in linear approximation of gravitational theory. We derive the analytical formulas and estimates for the metric perturbations and the radiated power of generated gravitational waves. Furthermore we investigate the characteristics of polarization and the behaviour of test particles in the presence of gravitational wave which will be important for the detection.

gr-qc↗

arXiv2015

Micro and nano patternable magnetic carbon

Carbon is conventionally not associated with magnetism, and much of the discussion of its nanotechnology perspectives appears to be centered on its electron transport properties. Among the few existing examples of magnetic carbon production, none has found a direct applicability in scalable micro and nano fabrication, Here we introduce a paramagnetic form of carbon whose precursor polymers can be lithographically patterned into micro and nano structures prior to pyrolysis. This unreactive and thermally robust material features strong room-temperature paramagnetism owing to a large number of unpaired electrons with restricted mobility, which is achieved by controlling the progression of bond dissociation and formation during pyrolysis. The manufacture of this magnetic carbon, having (3.97 x 0.8) 10^17 spins/ mg, can immediately benefit a number of spintronic and magnetic MEMS applications, and also shed light on the controversial theories concerning the existence and mechanisms of magnetism in carbon.

cond-mat.mtrl-sci↗

arXiv2014

Increased efficiency of ion acceleration by using femtosecond laser pulses at higher harmonic frequency

The influence of laser frequency on laser-driven ion acceleration is investigated by means of two-dimensional particle-in-cell simulations. When ultrashort intense laser pulse at higher harmonic frequency irradiates a thin solid foil, the target may become relativistically transparent for significantly lower laser pulse intensity compared to irradiation at fundamental laser frequency. The relativistically induced transparency results in an enhanced heating of hot electrons as well as increased maximum energies of accelerated ions and their numbers. Our simulation results have shown the increase of maximum proton energy and of the number of high-energy protons by a factor of 2 after the interaction of an ultrashort laser pulse of maximum intensity $7 \times 10^{21}~\rm{W/cm^2}$ with a fully ionized plastic foil of realistic density and of optimal thickness between $100~\rm{nm}$ and $200~\rm{nm}$ when switching from the fundamental frequency to the third harmonics.

physics.plasm-ph↗

arXiv2008

Time parameters and Lorentz transformations of relativistic stochastic processes

Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell distribution, the associated proper-time parameterized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy.

cond-mat.stat-mech↗