arXiv subjects

Thomas Schuster

Publications and source records attributed to Thomas Schuster.

At least 55 records · Page 3Linked to original sources

arXiv2021

A method for determining the parameters in a rheological model for viscoelastic materials by minimizing Tikhonov functionals

Mathematical models describing the behavior of viscoelastic materials are often based on evolution equations that measure the change in stress depending on its material parameters such as stiffness, viscosity or relaxation time. In this article, we introduce a Maxwell-based rheological model, define the associated forward operator and the inverse problem in order to determine the number of Maxwell elements and the material parameters of the underlying viscoelastic material. We perform a relaxation experiment by applying a strain to the material and measure the generated stress. Since the measured data varies with the number of Maxwell elements, the forward operator of the underlying inverse problem depends on parts of the solution. By introducing assumptions on the relaxation times, we propose a clustering algorithm to resolve this problem. We provide the calculations that are necessary for the minimization process and conclude with numerical results by investigating unperturbed as well as noisy data. We present different reconstruction approaches based on minimizing a least squares functional. Furthermore, we look at individual stress components to analyze different displacement rates. Finally, we study reconstructions with shortened data sets to obtain assertions on how long experiments have to be performed to identify conclusive material parameters.

math.NA↗

arXiv2020

Solving an inverse heat convection problem with an implicit forward operator by using a Projected Quasi-Newton method

We consider the quasilinear 1D inverse heat convection problem (IHCP) of determining the enthalpy-dependent heat fluxes from noisy internal enthalpy measurements. This problem arises in the Accelerated Cooling (ACC) process of producing thermomechanically controlled processed (TMCP) heavy plates made of steel. In order to adjust the complex microstructure of the underlying material, the Leidenfrost behavior of the hot surfaces with respect to the application of the cooling fluid has to be studied. Since the heat fluxes depend on the enthalpy and hence on the solution of the underlying initial boundary value problem (IBVP), the parameter-to-solution operator, and thus the forward operator of the inverse problem, can only be defined implicitly. To guarantee well-defined operators, we study two approaches for showing existence and uniqueness of solutions of the IBVP. One approach deals with the theory of pseudomonotone operators and so-called strong solutions in Sobolev-Bochner spaces. The other theory uses classical solutions in Hölder spaces. Whereas the first approach yields a solution under milder assumptions, it fails to show the uniqueness result in contrast to the second approach. Furthermore, we propose a convenient parametrization approach for the nonlinear heat fluxes in order to decouple the parameter-to-solution relation and use an iterative solver based on a Projected Quasi-Newton (PQN) method together with box-constraints to solve the inverse problem. For numerical experiments, we derive the necessary gradient information of the objective functional and use the discrepancy principle as a stopping rule. Numerical tests show that the PQN method outperforms the Landweber method with respect to computing time and approximation accuracy.

math.AP↗

arXiv2020

Speculative Dereferencing of Registers:Reviving Foreshadow

Since 2016, multiple microarchitectural attacks have exploited an effect that is attributed to prefetching. These works observe that certain user-space operations can fetch kernel addresses into the cache. Fetching user-inaccessible data into the cache enables KASLR breaks and assists various Meltdown-type attacks, especially Foreshadow. In this paper, we provide a systematic analysis of the root cause of this prefetching effect. While we confirm the empirical results of previous papers, we show that the attribution to a prefetching mechanism is fundamentally incorrect in all previous papers describing or exploiting this effect. In particular, neither the prefetch instruction nor other user-space instructions actually prefetch kernel addresses into the cache, leading to incorrect conclusions and ineffectiveness of proposed defenses. The effect exploited in all of these papers is, in fact, caused by speculative dereferencing of user-space registers in the kernel. Hence, mitigation techniques such as KAISER do not eliminate this leakage as previously believed. Beyond our thorough analysis of these previous works, we also demonstrate new attacks enabled by understanding the root cause, namely an address-translation attack in more restricted contexts, direct leakage of register values in certain scenarios, and the first end-to-end Foreshadow (L1TF) exploit targeting non-L1 data. The latter is effective even with the recommended Foreshadow mitigations enabled and thus revives the Foreshadow attack. We demonstrate that these dereferencing effects exist even on the most recent Intel CPUs with the latest hardware mitigations, and on CPUs previously believed to be unaffected, i.e., ARM, IBM, and AMD CPUs.

cs.CR↗

arXiv2019

Parameter estimation of temperature dependent material parameters in the cooling process of TMCP steel plates

Accelerated cooling is a key technology in producing thermomechanically controlled processed (TMCP) steel plates. In a TMCP process hot plates are subjected to a strong cooling what results in a complex microstructure leading to increased strength and fracture toughness. The microstructure is strongly affected by the temperature evolution during the cooling process as well as residual stresses and flatness deformations. Therefore, the full control (quantification) of the temperature evolution is very important regarding plate design and processing. It can only be achieved by a thermophysical characterization of the material and the cooling system. In this paper, we focus on the thermophysical characterization of the material parameters. Mathematically, we consider a specific inverse heat conduction problem. The temperature evolution of a heated steel plate passing through the cooling device is modeled by a 1D nonlinear partial differential equation (PDE) with unknown temperature dependent material parameters, which describe the characteristics of the underlying material. We present a numerical approach to identify these material parameters up to some canonical ambiguity without any a priori information.

math.NA↗

arXiv2019

Generalized attenuated ray transforms and their integral angular moments

In this article generalized attenuated ray transforms (ART) and integral angular moments are investigated. Starting from the Radon transform, the attenuated ray transform and the longitudinal ray transform, we derive the concept of ART-operators of order $k$ over functions defined on the phase space and depending on time. The ART-operators are generalized for complex-valued absorption coefficient as well as weight functions of polynomial and exponential type. Connections between ART operators of various orders are established by means of the application of the linear part of a transport equation. These connections lead to inhomogeneous differential equations of order $(k+1)$ for the ART of order $k$. Uniqueness theorems for the corresponding boundary-value and initial boundary-value problems are proved. Properties of integral angular moments of order $p$ are considered and connections between the moments of different orders are deduced. A close connection of the considered operators with mathematical models for tomography, physical optics and integral geometry allows to treat the inversion of ART of order $k$ as an inverse problem of determining the right-hand side of a corresponding differential equation.

math.NA↗

arXiv2019

Sequential subspace optimization for recovering stored energy functions in hyperelastic materials from time-dependent data

Monitoring structures of elastic materials for defect detection by means of ultrasound waves (Structural Health Monitoring, SHM) demands for an efficient computation of parameters which characterize their mechanical behavior. Hyperelasticity describes a nonlinear elastic behavior where the second Piola-Kirchhoff stress tensor is given as a derivative of a scalar function representing the stored (strain) energy. Since the stored energy encodes all mechanical properties of the underlying material, the inverse problem of computing this energy from measurements of the displacement field is very important regarding SHM. The mathematical model is represented by a high-dimensional parameter identification problem for a nonlinear, hyperbolic system with given initial and boundary values. Iterative methods for solving this problem, such as the Landweber iteration, are very time-consuming. The reason is the fact that such methods demand for several numerical solutions of the hyperbolic system in each iteration step. In this contribution we present an iterative method based on sequential subspace optimization (SESOP) which in general uses more than only one search direction per iteration and explicitly determines the step size. This leads to a significant acceleration compared to the Landweber method, even with only one search direction and an optimized step size. This is demonstrated by means of several numerical tests.

math.NA↗

arXiv2019

Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a tracer-based technique for medical imaging where the tracer consists of ironoxide nanoparticles. The key idea is to measure the particle response to a temporally changing external magnetic field to compute the spatial concentration of the tracer inside the object. A decent mathematical model demands for a data-driven computation of the system function which does not only describe the measurement geometry but also encodes the interaction of the particles with the external magnetic field. The physical model of this interaction is given by the Landau-Lifshitz-Gilbert (LLG) equation. The determination of the system function can be seen as an inverse problem of its own which can be interpreted as a calibration problem for MPI. In this contribution the calibration problem is formulated as an inverse parameter identification problem for the LLG equation. We give a detailed analysis of the direct as well as the inverse problem in an all-at-once as well as in a reduced setting. The analytical results yield a deeper understanding of inverse problems connected to the LLG equation and provide a starting point for the development of robust numerical solution methods in MPI.

math.AP↗

arXiv2019

Braiding photonic topological zero modes

A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states confined near topological defects, like Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the nontrivial phase that arises when such defects are "braided" around one another is not intrinsically quantum mechanical; rather, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, enabling the simulation of such phenomena in classical systems. Here we report the first experimental measurement in any system, quantum or classical, of the geometric phase due to such a braiding process. These measurements are obtained using an interferometer constructed from highly tunable 2D arrays of photonic waveguides. Our results introduce photonic lattices as a versatile playground for the experimental study of topological defects and their braiding, complementing ongoing efforts in solid-state systems and cold atomic gases.

physics.optics↗

arXiv2019

Scrambling and Complexity in Phase Space

The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: i) scrambling in the phase space of a single mode and ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct `types' of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out and quasi scrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.

quant-ph↗

arXiv2019

Floquet Hopf Insulators

We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf $\mathbb{Z}$ invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet $\mathbb{Z}_2$ invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time-evolution, subject to a process in which defects at different quasienergy exchange even amounts of topological charge. Their contrasting classifications lead to a measurable physical consequence, namely, an unusual bulk-boundary correspondence where gapless edge modes are topologically protected, but may exist at either 0- or $π$-quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators.

cond-mat.mes-hall↗

arXiv2018

Verified Quantum Information Scrambling

Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically $\sim80\%$, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

quant-ph↗

arXiv2017

Automated Detection, Exploitation, and Elimination of Double-Fetch Bugs using Modern CPU Features

Double-fetch bugs are a special type of race condition, where an unprivileged execution thread is able to change a memory location between the time-of-check and time-of-use of a privileged execution thread. If an unprivileged attacker changes the value at the right time, the privileged operation becomes inconsistent, leading to a change in control flow, and thus an escalation of privileges for the attacker. More severely, such double-fetch bugs can be introduced by the compiler, entirely invisible on the source-code level. We propose novel techniques to efficiently detect, exploit, and eliminate double-fetch bugs. We demonstrate the first combination of state-of-the-art cache attacks with kernel-fuzzing techniques to allow fully automated identification of double fetches. We demonstrate the first fully automated reliable detection and exploitation of double-fetch bugs, making manual analysis as in previous work superfluous. We show that cache-based triggers outperform state-of-the-art exploitation techniques significantly, leading to an exploitation success rate of up to 97%. Our modified fuzzer automatically detects double fetches and automatically narrows down this candidate set for double-fetch bugs to the exploitable ones. We present the first generic technique based on hardware transactional memory, to eliminate double-fetch bugs in a fully automated and transparent manner. We extend defensive programming techniques by retrofitting arbitrary code with automated double-fetch prevention, both in trusted execution environments as well as in syscalls, with a performance overhead below 1%.

cs.CR↗

arXiv2017

Identifying the stored energy of a hyperelastic structure by using an attenuated Landweber method

We consider the nonlinear, inverse problem of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field as well as from surface sensor measurements. The displacement field is represented as a solution of Cauchy's equation of motion, which is a nonlinear, elastic wave equation. Hyperelasticity means that the first Piola-Kirchhoff stress tensor is given as the gradient of the stored energy function. We assume that a dictionary of suitable functions is available and the aim is to recover the stored energy with respect to this dictionary. The considered inverse problem is of vital interest for the development of structural health monitoring systems which are constructed to detect defects in elastic materials from boundary measurements of the displacement field, since the stored energy encodes the mechanical peroperties of the underlying structure. In this article we develope a numerical solver for both settings using the attenuated Landweber method. We show that the parameter-to-solution map satisfies the local tangential cone condition. This result can be used to prove local convergence of the attenuated Landweber method in case that the full displacement field is measured. In our numerical experiments we demonstrate how to construct an appropriate dictionary and show that our algorithm is well suited to localize damages in various situations.

math.NA↗

arXiv2016

Non-Abelian braiding of light

Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially-fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.

cond-mat.mes-hall↗

arXiv2016

Dissipationless conductance in a topological coaxial cable

We present a dynamical mechanism leading to dissipationless conductance, whose quantized value is controllable, in a (3+1)-dimensional electronic system. The mechanism is exemplified by a theory of Weyl fermions coupled to a Higgs field--also known as an axion insulator. We show that the insertion of an axial gauge flux can induce vortex lines in the Higgs field, similarly to the development of vortices in a superconductor upon the insertion of magnetic flux. We further show that the necessary axial gauge flux can be generated using Rashba spin-orbit coupling or a magnetic field. Vortex lines in the Higgs field are known to bind chiral fermionic modes, each of which serves as a one-way channel for electric charge with conductance $e^2/h$. Combining these elements, we present a physical picture, the "topological coaxial cable," illustrating how the value of the quantized conductance could be controlled in such an axion insulator.

cond-mat.mes-hall↗

arXiv2016

An improved exact inversion formula for cone beam vector tomography

In this article we present an improved exact inversion formula for the 3D cone beam transform of vector fields. It is well known that only the solenoidal part of a vector field can be determined by the longitudinal ray transform of a vector field in cone beam geometry. The exact inversion formula, as it was developed in A. Katsevich and T. Schuster, 'An exact inversion formula for cone beam vector tomography', Inverse Problems 29 (2013), consists of two parts. the first part is of filtered backprojection type, whereas the second part is a costly 4D integration and very inefficient. In this article we tackle this second term and achieve an improvement which is easily to implement and saves one order of integration. The theory says that the first part contains all information about the curl of the field, whereas the second part presumably has information about the boundary values. This suggestion is supported by the fact that the second part vanishes if the exact field is divergence free and tangential at the boundary. A number of numerical tests, that are also subject of this article, confirm the theoretical results and the exactness of the formula.

math.NA↗

arXiv2016

Sequential subspace optimization for nonlinear inverse problems

In this work we discuss a method to adapt sequential subspace optimization (SESOP), which has so far been developed for linear inverse problems in Hilbert and Banach spaces, to the case of nonlinear inverse problems. We start by revising the well-known technique for Hilbert spaces. In a next step, we introduce a method using multiple search directions that are especially designed to fit the nonlinearity of the forward operator. To this end, we iteratively project the initial value onto stripes whose shape is determined by the search direction, the nonlinearity of the operator and the noise level. We additionally propose a fast algorithm that uses two search directions. Finally we will show convergence and regularization properties for the presented method.

math.NA↗

arXiv2016

A CG-type method in Banach spaces with an application to computerized tomography

Conjugate Gradient (CG) methods are one of the most effective iterative methods to solve linear equations in Hilbert spaces. So far, they have been inherently bound to these spaces since they make use of the inner product structure. In more general Banach spaces one of the most prominent iterative solvers are Landweber-type methods that essentially resemble the Steepest Descent method applied to the normal equation. More advanced are subspace methods that take up the idea of a Krylov-type search space, wherein an optimal solution is sought. However, they do not share the conjugacy property with CG methods. In this article we propose that the Sequential Subspace Optimization (SESOP) method can be considered as an extension of CG methods to Banach spaces. We employ metric projections to orthogonalize the current search direction with respect to the search space from the last iteration. For the l2-space our method then exactly coincides with the Polak-Ribière type of the CG method when applied to the normal equation. We show that such an orthogonalized search space still leads to weak convergence of the subspace method. Moreover, numerical experiments on a random matrix toy problem and 2D computerized tomography on lp-spaces show superior convergence properties over all p compared to non-orthogonalized search spaces. This especially holds for lp-spaces with small p. We see that the closer we are to an l2-space, the more we recover of the conjugacy property that holds in these spaces, i. e., as expected, the more the convergence behaves independently of the size of the truncated search space.

math.NA↗