Zero-dimensional Systems Research Articles

Degradation of Proton Exchange Membrane (PEM) Electrolysis: The Influence of Current Density

Hydrogen is expected to play an important role as a crosslinking technology between power generation on one hand and transport and industry on the other hand. It can directly replace fossil fuels in transport and industry when produced by water electrolysis renewable energies such as solar or wind, which are converted with low efficiencies. The relevant technologies are either the mature alkaline electrolysis or the newer proton exchange membrane (PEM) water electrolysis. The main advantage of PEM electrolysis technology is that it provides high efficiency, high power density with low footprint, and flexibility without the need of corrosive chemicals such as KOH (alkaline electrolysis). On the other hand, questions about degradation mechanisms, long-term stability and the high capital costs compared to the alkaline technology hinder the large-scale industrial penetration of this technology in the market. Moreover, these challenges are mutually dependent. Cost reductions of materials and stack components, for example, can have a negative impact on long-term stability. Thus, more information about the degradation mechanisms is necessary to determine an optimum between cost reduction and long-term stability. Furthermore, degradation measurements are expensive and evidently require a lot of time. Consequently, the development of accelerated stress tests (AST) protocols is in the focus of the current research by the academy and industry in particular. This presentation will discuss degradation processes of MEAs under high current density which has been found to accelerate degradation in our laboratory. Degradation was investigated in a HYLYZER™ Hydrogen Generator (HHG) from Hydrogenics under operation at 4 A cm-2 for almost 3000 h. The degradation of the bipolar plates and gas diffusion layers are neglected since these components are well protected against corrosion. The cells were analyzed by electrochemical impedance spectroscopy. Furthermore samples of ion exchange resin, which keeps the water resistivity above 10 MΩ, were collected and analyzed by XPS to quantify the accumulated ions. In addition, post-test investigations of the aged MEAs by conductive and material sensitive AFM, SEM with EDX and XPS were performed to identify degradation mechanisms. An important observation is a decrease of the ohmic resistance during operation at high current densities which is associated to fluoride release into the water. To analyze the time dependence of the cells in the hydrogen generator system a zero-dimensional system model with effective parameters was developed. This model enables quantifying the degradation measurements and the discussion in the context of system behavior. Preventing metal oxidation by corrosion protective layers leads to increased efficiency mainly due to decreasing ohmic resistances. This decrease is assumed to be depending on current density and time. The observed F release rate supports this conclusion. The degradation mechanism is assumed to be an increased permeability for water, oxygen and hydrogen with corresponds to a membrane thinning and ionomer loss in the electrodes. Such an interpretation was backed by the ex-situ post-test analysis. At the anodes a general increase of conductive area fraction evaluated by AFM indicates a loss of ionomer. At the cathodes, a general decrease of conductive area fraction indicates a loss of catalysts. EDX confirmed the loss of Pt and Ir from cathode and anode respectively, and in addition a loss of Ti from the anode was found. Membrane thinning occurred in all cells. It is explained by ionomer decomposition catalyzed by the well distributed Pt content in the membranes detected by XPS. Acknowledgements The research leading to these results has received funding from the European Union’s Seventh Framework Program (FP7/ 2007-2013) for the Fuel Cells and Hydrogen Joint Technology Initiative under grant n° 621237, “ INSIDE- In -situ Diagnostics in Water Electrolyzers“ and from national projects “LastElSys” and “WESpe” by Federal Ministry for Economic Affairs and Energy. Figure 1

Uniform Generators, Symbolic Extensions with an Embedding, and Structure of Periodic Orbits

For a topological dynamical system $$(X,T)$$ we define a uniform generator as a finite measurable partition such that the symmetric cylinder sets in the generated process shrink in diameter uniformly to zero. The problem of existence and optimal cardinality of uniform generators has lead us to new challenges in the theory of symbolic extensions. At the beginning we show that uniform generators can be identified with so-called symbolic extensions with an embedding, i.e., symbolic extensions admitting an equivariant measurable selector from preimages. From here we focus on such extensions and we strive to characterize the collection of the corresponding extension entropy functions on invariant measures. For aperiodic zero-dimensional systems we show that this collection coincides with that of extension entropy functions in arbitrary symbolic extensions, which, by the general theory of symbolic extensions, is known to coincide with the collection of all affine superenvelopes of the entropy structure of the system. In particular, we recover, after Burguet (Monatsh Math 184:21–49, 2017), that an aperiodic zero-dimensional system is asymptotically h-expansive if and only if it admits an isomorphic symbolic extension. Next we pass to systems with periodic points, and we introduce the notion of a period tail structure, which captures the local growth rate of periodic orbits. Finally, we succeed in precisely identifying the wanted collection of extension entropy functions in symbolic extensions with an embedding: these are all the affine superenvelopes of the usual entropy structure which lie above certain threshold function determined by the period tail structure. This characterization allows us, among other things, to give estimates (and in examples to compute precisely) of the optimal cardinality of a uniform generator. As a byproduct, we prove a theorem saying that every zero-dimensional system admits an aperiodic zero-dimensional extension which is isomorphic on aperiodic measures and otherwise principal (periodic measures lift to measures of entropy zero).

A zero-dimensional topologically nontrivial state in a superconducting quantum dot.

The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., systems with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the presence of zero-energy modes and discontinuities in the current–phase relation at zero temperature. These fermion parity transitions therefore can be revealed by the current discontinuities or by a measure of the critical current at low temperatures.

Mechanical topological insulator in zero dimensions

We study linear vibrational modes in finite isostatic Maxwell lattices, mechanical systems where the number of degrees of freedom matches the number of constraints. Recent progress in topological mechanics exploits the nontrivial topology of BDI class Hamiltonians in one dimenson and arising topological floppy modes at the edges. A finite frame, or zero-dimensional system, also exhibits a nonzero topological index according to the classification table. We construct mechanical insulating models in zero dimensions that complete the BDI classification in the available real space dimensions. We compute and interpret its nontrivial invariant ${\mathbb{Z}}_{2}$.

The point decomposition problem over hyperelliptic curves

Computing discrete logarithms is generically a difficult problem. For divisor class groups of curves defined over extension fields, a variant of the Index-Calculus called Decomposition attack is used, and it can be faster than generic approaches. In this situation, collecting the relations is done by solving multiple instances of the Point m-Decomposition Problem (PDP$_m$). An instance of this problem can be modelled as a zero-dimensional polynomial system. Solving is done with Grobner bases algorithms, where the number of solutions of the system is a good indicator for the time complexity of the solving process. For systems arising from a PDP$_m$ context, this number grows exponentially fast with the extension degree. To achieve an efficient harvesting, this number must be reduced as much as as possible. Extending the elliptic case, we introduce a notion of Summation Ideals to describe PDP m instances over higher genus curves, and compare to Nagao's general approach to PDP$_m$ solving. In even characteristic we obtain reductions of the number of solutions for both approaches, depending on the curve's equation. In the best cases, for a hyperelliptic curve of genus $g$, we can divide the number of solutions by $2^{(n−1)(g+1)}$. For instance, for a type II genus 2 curve defined over $\mathbb{F}_{2^{93}}$ whose divisor class group has cardinality a near-prime 184 bits integer, the number of solutions is reduced from 4096 to 64. This is enough to build the matrix of relations in around 7 days with 8000 cores using a dedicated implementation.

Phonon-induced dissipation and decoherence in solid-state quantum devices: Markovian versus non-Markovian treatments

Microscopic modeling of electronic phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this context, non-Markovian density-matrix approaches are widely used simulation strategies. Here we show that such methods, along with valuable virtues, in some circumstances may exhibit potential limitations that need to be taken into account for a reliable description of quantum materials and related devices. More specifically, extending the analysis recently proposed in [EPL 112, 67005 (2015)] to high temperatures and degenerate conditions, we show that the usual mean-field treatment – employed to derive quantum-kinetic equations – in some cases may lead to anomalous results, characterized by decoherence suppression and positivity violations. By means of a simple two-level model, we show that such unexpected behaviors may affect zero-dimensional electronic systems coupled to dispersionless phonon modes, while such anomalies are expected to play a negligible role in nanosystems with higher dimensionality; these limitations are found to be significant in the low-density and low-temperature limit, while in the degenerate and/or finite-temperature regime – typical of many state-of-the-art quantum devices – their impact is strongly reduced.

Faces of simplices of invariant measures for actions of amenable groups

We extend the result of Downarowicz (Israel J Math 165:189–210, 2008) to the case of amenable group actions, by showing that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group G can be modeled as the entire simplex of invariant measures on some other zero-dimensional dynamical system with free action of G. This is a continuation of our investigations from Frej and Huczek (Groups Geom Dyn 11:567–583, 2017), inspired by an earlier paper (Downarowicz in Israel J Math 156:93–110, 2006).

Near-Field Raman Enhancement of Single Molecules and Point Scatterers

Tip-enhanced Raman spectroscopy (TERS) is an emerging tool to characterize low-dimensional materials requiring high spatial resolution beyond the light diffraction limit. The most extreme example of a spatially localized scatterer is that of a zero-dimensional system, e.g., a single molecule, a nanoparticle, or an individual defect within a crystal. Here, using an analytical model for near-field Raman scattering from point-like structures in the presence of a plasmonic metal probe, we investigate the TERS patterns of representative single molecules with arbitrary orientation, for a range of Raman tensor symmetries. The results can be used to determine the orientation of single molecules as well as to differentiate molecules with diverse Raman tensors or, conversely, Raman modes with different Raman tensors from the same molecule. To demonstrate that the model is of general applicability to any spatially localized Raman modes, we further apply it to TERS imaging of individual point defects in graphene, unv...

Rank 2 proximal Cantor systems are residually scrambled

ABSTRACTDownarowicz and Maass [7] proposed topological ranks for all homeomorphic Cantor minimal dynamical systems using properly ordered Bratteli diagrams. In this study, we adopt this definition to the case of the essentially minimal zero-dimensional systems. We consider the cases in which topological ranks are 2 and unique minimal sets are fixed points. Akin and Kolyada [2], had shown that if the unique minimal set of an essentially minimal system is a fixed point, then the system must be proximal. The finite topological rank implies expansiveness; furthermore, in the case of proximal Cantor systems with topological rank 2, the expansiveness is always from the lowest degree. Rank 2 proximal Cantor systems are residually scrambled. We present a necessary and sufficient condition for the unique ergodicity of these systems. In addition, we show that the number of ergodic measures of the systems that are topologically mixing can be 1 and 2. Moreover, we present examples that are topologically weakly mixing, not topologically mixing, and uniquely ergodic. Finally, we show that the number of ergodic measures of the systems that are not weakly mixing can be 1 and 2.

On the last fall degree of zero-dimensional Weil descent systems

In this article we will discuss a mostly theoretical framework for solving zero-dimensional polynomial systems. Complexity bounds are obtained for solving such systems using a new parameter, called the last fall degree, which does not depend on the choice of a monomial order. The method is similar to certain MutantXL algorithms, but our abstract formulation has advantages. For example, we can prove that the cryptographic systems multi-HFE and HFE are insecure.More generally, let k be a finite field of cardinality qn and let k′ be the subfield of cardinality q. Let F⊂k[X0,…,Xm−1] be a finite subset generating a zero-dimensional ideal. We give an upper bound of the last fall degree of the Weil descent system of F from k to k′, which depends on q, m, the last fall degree of F, the degree of F and the number of solutions of F, but not on n. This shows that such Weil descent systems can be solved efficiently if n grows and the other parameters are fixed. In particular, one can apply these results to show a weakness in the cryptographic protocols HFE and multi-HFE.

Explicit H∞ controllers for 1st to 3rd order single-input single-output systems with parameters

The purpose of this paper is to explicitly characterize H∞ controllers for single-input single-output (SISO) systems of order 1, 2 and 3 in terms of their coefficients considered as unknown parameters. In the SISO case, computing H∞ controllers requires to find the real positive definite solution of an algebraic Riccati equation. Due to the system parameters, no purely numerical method can be used to find such a solution, and thus parametric H∞ controllers. Using elimination techniques of zero-dimensional polynomial systems, we first give a parametrization of all the solutions of the algebraic Riccati equation associated with the H∞ control problem. Since the problem reduces to solving an univariate polynomial of degree less than or equal to 4, closed-form solutions are then obtained for the solutions of the algebraic Riccati equation by means of radicals. Using the concept of discriminant variety, we show that the maximal real root of this polynomial is always defined by the same closed-form expression, which yields the positive definite solution of the algebraic Riccati equation. Finally, we use the above results to explicitly compute the H∞ criteria γpt and H∞ controllers in terms of the system parameters and study them with respect to parameter variations.

Explicit H∞ controllers for 4th order single-input single-output systems with parameters and their application to the two mass-spring system with damping

The purpose of this paper is to explicitly characterize H∞ controllers for 4th order single-input single-output (SISO) systems in terms of their coefficients considered as unknown parameters. In the SISO case, computing H∞ controllers requires to find the real positive definite solution of an algebraic Riccati equation (ARE). Due to the system parameters, no purely numerical method can be used to find such a solution, and thus parametric H∞ controllers. Using elimination techniques for zero-dimensional polynomial systems, we first give a rational parametrization of all the solutions of the ARE. Then, as the problem reduces to solving polynomials of degree 4, closed-form solutions are obtained for all the solutions of this ARE by using expressions by radicals. Using the concept of discriminant variety, we then show that the maximal real root of one of these polynomials is encoded by two different closed-form expressions depending on the values of the system parameters, which yields to different positive definite solution of the ARE. The above results are then used to explicitly compute the H∞ criterion γopt and H∞ controllers in terms of the system parameters. Finally, we study in detail a particular system: the two-mass-spring system with damping. Due to the low number of parameters, we can plot the variations of γopt in function of the parameters, compute approximations of γopt at a working point, and derive the expression of a weight function of the parameters to set γopt to a desired value.

Finite-rank Bratteli–Vershik homeomorphisms are expansive

Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank $K > 1$ is expansive. Bezuglyi, Kwiatkowski, and Medynets (2009) extended the result to non-minimal aperiodic cases. In this paper, we show that all finite-rank zero-dimensional systems are expansive or have infinite odometer systems; this is an extension of the two aforementioned results. Nevertheless, the methods follow similar approaches.

Correlated fluorescence blinking in two-dimensional semiconductor heterostructures.

'Blinking', or 'fluorescence intermittency', refers to a random switching between 'ON' (bright) and 'OFF' (dark) states of an emitter; it has been studied widely in zero-dimensional quantum dots and molecules, and scarcely in one-dimensional systems. A generally accepted mechanism for blinking in quantum dots involves random switching between neutral and charged states (or is accompanied by fluctuations in charge-carrier traps), which substantially alters the dynamics of radiative and non-radiative decay. Here, we uncover a new type of blinking effect in vertically stacked, two-dimensional semiconductor heterostructures, which consist of two distinct monolayers of transition metal dichalcogenides (TMDs) that are weakly coupled by van der Waals forces. Unlike zero-dimensional or one-dimensional systems, two-dimensional TMD heterostructures show a correlated blinking effect, comprising randomly switching bright, neutral and dark states. Fluorescence cross-correlation spectroscopy analyses show that a bright state occurring in one monolayer will simultaneously lead to a dark state in the other monolayer, owing to an intermittent interlayer carrier-transfer process. Our findings suggest that bilayer van der Waals heterostructures provide unique platforms for the study of charge-transfer dynamics and non-equilibrium-state physics, and could see application as correlated light emitters in quantum technology.

A universal explanation of tunneling conductance in exotic superconductors

A longstanding mystery in understanding cuprate superconductors is the inconsistency between the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we reconcile the two experimental techniques by generalising a theory which was previously applied to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic superconductors. We show that the side peaks observed in tunneling conductance measurements in all these materials have a universal origin: They are formed by coherence-mediated tunneling under bias and do not directly reflect the underlying density of states (DOS) of the sample. We obtain theoretical predictions of the tunneling conductance and the density of states of the sample simultaneously and show that for cuprate and pnictide superconductors, the extracted sample DOS is consistent with the superconducting gap measured by ARPES.

Electron–phonon dissipation in quantum nanodevices

Microscopic modelling of electronic-phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this context, a variety of simulation strategies have been proposed and employed. The aim of this article is to discuss virtues versus intrinsic limitations of non-Markovian density-matrix approaches. More specifically, we shall show that the usual mean-field treatment employed to derive quantum-kinetic equations may lead to highly unphysical results, like negative distribution functions and non-dissipative carrier---optical phonon couplings. By means of a simple two-level model, we shall show that such limitations are expected to be particularly severe in zero-dimensional electronic systems--like quantum-dot nanostructures, potential constituents of quantum-computation devices--coupled to dispersionless phonon modes. Such a behaviour is in striking contrast with the case of Markovian treatments, where a proper combination of adiabatic limit and mean-field approximation guarantees a physically acceptable solution.

Combinatorial embedding of chain transitive zero-dimensional systems into chaos

In this paper, we construct examples of transitive Li–Yorke chaotic zero-dimensional topological dynamical systems, which should be able to accommodate of a variety of subsystems. In fact, we show that a zero-dimensional chain transitive dynamical system can be embedded into a transitive Li–Yorke chaotic system with a dense scrambled set, and with the same topological entropy. Our work reflects the notion of uniform chaos, which was recently developed. In addition, our work reflects the recent work of invariance of scrambled sets in general topological setting. In these works, Mycielski sets play an essential role. Actually, we concretely construct a Mycielski set K such that it is densely uniformly chaotic, and also invariant in both directions. Furthermore, every point in K is positively and negatively transitive. The uniform proximality and recurrence of K are also bidirectional.

Phenomenological theory of optical broadening in zero-dimensional systems applied to silicon nanocrystals

We develop a phenomenological theory of inhomogeneous broadening in zero-dimensional systems and apply it to study photoluminescence (PL) spectra of silicon nanocrystals measured at helium and room temperatures. The proposed approach allowed us to explain experimentally observed PL peak asymmetry, linear dependence of the peak width on its maximum, and anomalous alteration of spectral characteristics with temperature increase.

Exploration of one-dimensional plasma current density profile for K-DEMO steady-state operation

Concept study for Korean demonstration fusion reactor (K-DEMO) is in progress, and basic design parameters are proposed by targeting high magnetic field operation with ITER-sized machine. High magnetic field operation is a favorable approach to enlarge relative plasma performance without increasing normalized beta or plasma current. Exploration of one-dimensional current density profile and its optimization process for the K-DEMO steady-state operation are reported in this paper. Numerical analysis is conducted with an integrated plasma simulation code package incorporating a transport code with equilibrium and current drive modules. Operation regimes are addressed with zero-dimensional system analysis. One-dimensional plasma current density profile is calculated based on equilibrium, bootstrap current analysis, and thermal transport analysis. The impact of self and external heating profiles on those parameters is considered self-consistently, where thermal power balance and 100% non-inductive current drive are the main constraints during the whole exploration procedure. Current and pressure profiles are identified as a reference steady-state profile by minimizing the external heating power with desired fusion power.

Heterodimensional charge-carrier confinement in stacked submonolayer InAs in GaAs

Charge-carrier confinement in nanoscale In-rich agglomerations within a lateral InGaAs quantum well (QW) formed from stacked submonolayers (SMLs) of InAs in GaAs is studied. Low-temperature photoluminescence (PL) and magneto-PL clearly demonstrate strong vertical and weak lateral confinement, yielding two-dimensional (2D) excitons. In contrast, high-temperature (400 K) magneto-PL reveals excited states that fit a Fock-Darwin spectrum, characteristic of a zero-dimensional (0D) system in a magnetic field. This paradox is resolved by concluding that the system is heterodimensional: the light electrons extend over several In-rich agglomerations and see only the lateral InGaAs QW, i.e., are 2D, while the heavier holes are confined within the In-rich agglomerations, i.e., are 0D. This description is supported by single-particle effective-mass and eight-band k⋅p calculations. We suggest that the heterodimensional nature of nanoscale SML inclusions is fundamental to the ability of respective optoelectronic devices to operate efficiently and at high speed.