Nematic-Isotropic Interfaces Under Shear: A Molecular Dynamics Simulation

We present a large-scale molecular dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with Lees-Edwards boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry breaking) flow in the {\em vorticity} direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.Comment: to appear in J. Chem. Phy

Random numbers from the tails of probability distributions using the transformation method

The speed of many one-line transformation methods for the production of, for example, Levy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, is very high and satisfactory for most purposes. However, for the class of decreasing probability densities fast rejection implementations like the Ziggurat by Marsaglia and Tsang promise a significant speed-up if it is possible to complement them with a method that samples the tails of the infinite support. This requires the fast generation of random numbers greater or smaller than a certain value. We present a method to achieve this, and also to generate random numbers within any arbitrary interval. We demonstrate the method showing the properties of the transform maps of the above mentioned distributions as examples of stable and geometric stable random numbers used for the stochastic solution of the space-time fractional diffusion equation.Comment: 17 pages, 7 figures, submitted to a peer-reviewed journa

Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Levy stable random variables and validate it by Monte Carlo simulation.Comment: 10 pages, 1 figure, submitted to Eur. Phys. J.

Sentiment trading with large language models

We analyse the performance of the large language models (LLMs) OPT, BERT, and FinBERT, alongside the traditional Loughran-McDonald dictionary, in the sentiment analysis of 965,375 U.S. financial news articles from 2010 to 2023. Our findings reveal that the GPT-3-based OPT model significantly outperforms the others, predicting stock market returns with an accuracy of 74.4%. A long-short strategy based on OPT, accounting for 10 basis points (bps) in transaction costs, yields an exceptional Sharpe ratio of 3.05. From August 2021 to July 2023, this strategy produces an impressive 355% gain, outperforming other strategies and traditional market portfolios. This underscores the transformative potential of LLMs in financial market prediction and portfolio management and the necessity of employing sophisticated language models to develop effective investment strategies based on news sentiment

Stochastic integration for uncoupled continuous-time random walks

Continuous-time random walks are pure-jump processes with several applications in physics, but also in insurance, finance and economics. Based on heuristic considerations, a definition is given for the stochastic integral driven by continuous-time random walks. The martingale properties of the integral are investigated. Finally, it is shown how the definition can be used to easily compute the stochastic integral by means of Monte Carlo simulations.Continuous-time random walks; models of tick-by-tick financial data; stochastic integration

Large scale simulation of synthetic markets

High-frequency trading has been experiencing an increase of interest both for practical purposes within financial institutions and within academic research; recently, the UK Government Office for Science reviewed the state of the art and gave an outlook analysis. Therefore, models for tick-by-tick financial time series are becoming more and more important. Together with high-frequency trading comes the need for fast simulations of full synthetic markets for several purposes including scenario analyses for risk evaluation. These simulations are very suitable to be run on massively parallel architectures. Aside more traditional large-scale parallel computers, high-end personal computers equipped with several multi-core CPUs and general-purpose GPU programming are gaining importance as cheap and easily available alternatives. A further option are FPGAs. In all cases, development can be done in a unified framework with standard C or C++ code and calls to appropriate libraries like MPI (for CPUs) or CUDA for (GPGPUs). Here we present such a prototype simulation of a synthetic regulated equity market. The basic ingredients to build a synthetic share are two sequences of random variables, one for the inter-trade durations and one for the tick-by-tick logarithmic returns. Our extensive simulations are based on several distributional choices for the above random variables, including Mittag-Leffler distributed inter-trade durations and alpha-stable tick-by-tick logarithmic returns

New Imaging Protocols for New Single Photon Emission CT Technologies

Nuclear cardiology practitioners have several new technologies available with which to perform myocardial perfusion single photon emission CT (MPS). These include dedicated small-footprint cardiac scanners, new stationary or semi-stationary three-dimensional detectors, and advanced software algorithms for optimal image reconstruction. These new technologies have been employed to reduce imaging time and radiation exposure. They require less technologist and camera time and offer improved patient comfort. They have potential for the overall cost reduction of MPS and at the same time for improved accuracy by increased resolution, or accurate attenuation correction. Furthermore, these new technologies offer potential for new protocols such as simultaneous dual isotope, new combinations of isotopes, stress only MPS, or dynamic first-pass imaging. In addition, new imaging technologies in coronary CT angiography (CCTA) allow novel hybrid stress only MPS/CCTA protocols with reduced radiation burden. Additional developments further improving efficiency and diagnostic accuracy of MPS are on the horizon

Expressions for forces and torques in molecular simulations using rigid bodies

Expressions for intermolecular forces and torques, derived from pair potentials between rigid non-spherical units, are presented. The aim is to give compact and clear expressions, which are easily generalised, and which minimise the risk of error in writing molecular dynamics simulation programs. It is anticipated that these expressions will be useful in the simulation of liquid crystalline systems, and in coarse-grained modelling of macromolecules

Velocity and energy distributions in microcanonical ensembles of hard spheres

In a microcanonical ensemble (constant $NVE$, hard reflecting walls) and in a molecular dynamics ensemble (constant $NVE\mathbf{PG}$, periodic boundary conditions) with a number $N$ of smooth elastic hard spheres in a $d$-dimensional volume $V$ having a total energy $E$, a total momentum $\mathbf{P}$, and an overall center of mass position $\mathbf{G}$, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on $d$, $N$, $E$, the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in $d$ dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of $N$.Comment: 11 pages, 3 figure