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We derive an expression for the tensor polarization of a system of massive spin-1 particles in a hydrodynamic framework. Starting from quantum kinetic theory based on the Wigner-function formalism, we employ a modified method of moments which also takes into account all spin degrees of freedom. It is shown that the tensor polarization of an uncharged fluid is determined by the shear-stress tensor. In order to quantify this novel polarization effect, we provide a formula which can be used for numerical calculations of vector-meson spin alignment in relativistic heavy-ion collisions.
Focused electron-beam-induced deposition (FEBID) is a highly versatile direct-write approach with particular strengths in the 3D nanofabrication of functional materials. Despite its apparent similarity to other 3D printing approaches, non-local effects related to precursor depletion, electron scattering and sample heating during the 3D growth process complicate the shape-true transfer from a target 3D model to the actual deposit. Here, we describe an efficient and fast numerical approach to simulate the growth process, which allows for a systematic study of the influence of the most important growth parameters on the resulting shape of the 3D structures. The precursor parameter set derived in this work for the precursor Me3PtCpMe enables a detailed replication of the experimentally fabricated nanostructure, taking beam-induced heating into account. The modular character of the simulation approach allows for additional future performance increases using parallelization or drawing on the use of graphics cards. Ultimately, beam-control pattern generation for 3D FEBID will profit from being routinely combined with this fast simulation approach for optimized shape transfer.
Nowadays, teachers are facing a more and more digitized world, as digital tools are being used by their students on a daily basis. This requires digital competencies in order to react in a professional manner to individual and societal challenges and to teach the students a purposeful use of those tools. Regarding the subject (e.g., STEM), this purpose includes specific content aspects, like data processing, or modeling and simulations of complex scientific phenomena. Yet, both pre-service and experienced teachers often consider their digital teaching competencies insufficient and wish for guidance in this field. Especially regarding immersive tools like augmented reality (AR), they do not have a lot of experience, although their willingness to use those modern tools in their lessons is high. The digital tool AR can target another problem in science lessons: students and teachers often have difficulties with understanding and creating scientific models. However, these are a main part of the scientific way of acquiring knowledge and are therefore embedded in curricula. With AR, virtual visualizations of model aspects can be superimposed on real experimental backgrounds in real time. It can help link models and experiments, which usually are not part of the same lesson and are perceived differently by students. Within the project diMEx (digital competencies in modeling and experimenting), a continuing professional development (CPD) for physics teachers was planned and conducted. Secondary school physics educators were guided in using AR in their lessons and their digital and modeling competencies for a purposeful use of AR experiments were promoted. To measure those competencies, various instruments with mixed methods were developed and evaluated. Among others, the teachers’ digital competencies have been assessed by four experts with an evaluation matrix based on the TPACK model. Technological, technical and design aspects as well as the didactical use of an AR experiment were assessed. The teachers generally demonstrate a high level of competency, especially in the first-mentioned aspects, and have successfully implemented their learnings from the CPD in the (re)design of their AR experiments.
The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules, the photoelectron energy does not depend on the electron’s emission direction, but theoretical studies have questioned this since 1990. Here, we provide experimental evidence that the energies of photoelectrons emitted against the light propagation direction are shifted toward higher values, while those electrons that are emitted along the light propagation direction are shifted to lower values. We attribute the energy shift to a nondipole contribution to the ponderomotive potential that is due to the interaction of the moving electrons with the incident photons.
We fabricated memristive devices using focused electron beam-induced deposition (FEBID) as a direct-writing technique employing a Pt/TiO2/Pt sandwich layer device configuration. Pinching in the measured current-voltage characteristics (i-v), the characteristic fingerprint of memristive behavior was clearly observed. The temperature dependence was measured for both high and low resistive states in the range from 290 K down to about 2 K, showing a stretched exponential behavior characteristic of Mott-type variable-range hopping. From this observation, a valence change mechanism of the charge transport inside the TiO2 layer can be deduced.
Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities
(2021)
The distinct ways the COVID-19 pandemic has been unfolding in different countries and regions suggest that local societal and governmental structures play an important role not only for the baseline infection rate, but also for short and long-term reactions to the outbreak. We propose to investigate the question of how societies as a whole, and governments in particular, modulate the dynamics of a novel epidemic using a generalization of the SIR model, the reactive SIR (short-term and long-term reaction) model. We posit that containment measures are equivalent to a feedback between the status of the outbreak and the reproduction factor. Short-term reaction to an outbreak corresponds in this framework to the reaction of governments and individuals to daily cases and fatalities. The reaction to the cumulative number of cases or deaths, and not to daily numbers, is captured in contrast by long-term reaction. We present the exact phase space solution of the controlled SIR model and use it to quantify containment policies for a large number of countries in terms of short and long-term control parameters. We find increased contributions of long-term control for countries and regions in which the outbreak was suppressed substantially together with a strong correlation between the strength of societal and governmental policies and the time needed to contain COVID-19 outbreaks. Furthermore, for numerous countries and regions we identified a predictive relation between the number of fatalities within a fixed period before and after the peak of daily fatality counts, which allows to gauge the cumulative medical load of COVID-19 outbreaks that should be expected after the peak. These results suggest that the proposed model is applicable not only for understanding the outbreak dynamics, but also for predicting future cases and fatalities once the effectiveness of outbreak suppression policies is established with sufficient certainty. Finally, we provide a web app (https://itp.uni-frankfurt.de/covid-19/) with tools for visualising the phase space representation of real-world COVID-19 data and for exporting the preprocessed data for further analysis.
Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius toward the desired value. For both mechanisms the spectral radius is autonomously adapted while the network receives and processes inputs under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols. Moreover, we evaluated the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using set point homeostatic feedback controls of neural firing.
Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel–Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel–Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality, H(a(t)), where H(t) is the Hubble parameter and a(t) is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time t. For Eckart-type viscous background, especially at finite cosmological constant, non-singular H(t) and a(t) are obtained, where H(t) diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of H(a(t)) is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing H(a(t)) with increasing a(t) varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure.
Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait –the propensity to compare one’s own success with that of others– expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.
Quantum discontinuity fixed point and renormalization group flow of the Sachdev-Ye-Kitaev model
(2021)
We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. From a controlled truncation of the infinite hierarchy of the exact functional RG flow equations, we identify several fixed points. Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum first-order transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of the transition in terms of a local effective Ising variable as is established for classical transitions. We propose an entangled quantum state at phase coexistence as a possible physical origin of this critical behavior.