Microstructured materials, such as architected metamaterials and phononic crystals, exhibit complex wave propagation phenomena due to their internal structure. While full-scale numerical simulations can capture these effects, they are computationally demanding, especially in time-domain analyses. To overcome this limitation, effective continuum models have been developed to approximate the macroscopic behavior of these materials while retaining key microscale effects. In this work we investigate the time-domain dynamic response of microstructured materials and focus on their effective micromorphic counterparts. We compare direct numerical simulations of discrete microstructures with predictions from micromorphic models to assess their accuracy in capturing transient wave phenomena. Our findings provide new insights into the applicability and limitations of micromorphic models in time-dependent analyses, contributing to the development of improved predictive tools for metamaterial design and engineering applications.
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks typically use spherical harmonics as angular basis functions, and then use Clebsch-Gordan contraction to maintain rotational symmetry, which may introduce redundancies in representations and computational overhead. We propose an alternative: a Cartesian-coordinates-based atomic density expansion. This approach provides a complete set of polynormially indepedent features of atomic environments while maintaining interaction body orders. Additionally, we integrate low-dimensional embeddings of various chemical elements and inter-atomic message passing. The resulting potential, named Cartesian Atomic Cluster Expansion (CACE), exhibits good accuracy, stability, and generalizability. We validate its performance in diverse systems, including bulk water, small molecules, and 25-element high-entropy alloys.
Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network architectures, the training becomes more difficult and expensive, which may have a counterproductive effect on the accuracy of calculation. In this work, we propose to make use of the training data to perform variance extrapolation when using neural-network ansatz in variational Monte Carlo. We show that this approach can speed up the convergence and surpass the ansatz limitation to obtain an improved estimation of the energy. Moreover, variance extrapolation greatly enhances the error cancellation capability, resulting in significantly improved relative energy outcomes, which are the keys to chemistry and physics problems.
The Vlasov-Maxwell equations provide an \textit{ab-initio} description of collisionless plasmas, but solving them is often impractical because of the wide range of spatial and temporal scales that must be resolved and the high dimensionality of the problem. In this work, we present a quantum-inspired semi-implicit Vlasov-Maxwell solver that utilizes the quantized tensor network (QTN) framework. With this QTN solver, the cost of grid-based numerical simulation of size $N$ is reduced from $\mathcal{O}(N)$ to $\mathcal{O}(\text{poly}(D))$, where $D$ is the ``rank'' or ``bond dimension'' of the QTN and is typically set to be much smaller than $N$. We find that for the five-dimensional test problems considered here, a modest $D=64$ appears to be sufficient for capturing the expected physics despite the simulations using a total of $N=2^{36}$ grid points, \edit{which would require $D=2^{18}$ for full-rank calculations}. Additionally, we observe that a QTN time evolution scheme based on the Dirac-Frenkel variational principle allows one to use somewhat larger time steps than prescribed by the Courant-Friedrichs-Lewy (CFL) constraint. As such, this work demonstrates that the QTN format is a promising means of approximately solving the Vlasov-Maxwell equations with significantly reduced cost.
The ability to model and sample from conditional densities is important in many physics applications. Implicit quantile networks (IQN) have been successfully applied to this task in domains outside physics. In this work, we illustrate the potential of IQNs as components of emulators using the simulation of jets as an example. Specifically, we use an IQN to map jets described by their 4-momenta at the generation level to jets at the event reconstruction level. The conditional densities emulated by our model closely match those generated by $\texttt{Delphes}$, while also enabling faster jet simulation.
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions. Conceptually, the population flow between cities closely resembles the random walk of a single walker in a state space. We start from two states, then three states, and finally the setup is fully generalized to many states of both discrete and continuous distributions. Despite the mathematical simplicity, the setup remarkably includes all the essential concepts of Markov Chain Monte Carlo without loss of generality, e.g., ergodicity, global balance and detailed balance, proposal or selection probability, acceptance probability, up to the underlying stochastic matrix, and error analysis. Our teaching experience suggests that most senior undergraduate students in physics can closely follow these materials without much difficulty.
Abstract The paper comprises an (s,S) production inventory facility in which multiple vacations and varying service rates are considered for the multiple servers. The arrival of customers constitutes a Markovian Arrival Process (MAP) and service completion times follow the phase type distributions with representations ( α, S ) and ( β, T ) respectively. Manufacturing needs to begin at the moment when the stock position falls to s. Service is offered at a lower rate if the stock level ranges from 0 to s and the service time distribution has the representations (α, η 1 S) and (β, η 2 T ), 0 < η 1, η 2 < 1 respectively. If the stock level reaches the maximum S, production is ceased to operate. 1-limited service policy, Bernoulli service schedule, and Exhaustive service disciplines are considered for the servers. A suitable cost function is outlined as per performance assessment. The impact of negative correlated inter arrival times on cost function is illustrated. Also, a relative study of expected cost function on different service modes is presented.
The parameters tuning of event generators is a research topic characterized by complex choices: the generator response to parameter variations is difficult to obtain on a theoretical basis, and numerical methods are hardly tractable due to the long computational times required by generators. Event generator tuning has been tackled by parametrisation-based techniques, with the most successful one being a polynomial parametrisation. In this work, an implementation of tuning procedures based on artificial neural networks is proposed. The implementation was tested with closure testing and experimental measurements from the ATLAS experiment at the Large Hadron Collider.
To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals. The simplest way to compose the basis is to choose a finite set of single-particle wave functions and find all possible distributions of a given number of particles in these states. It is known, however, that this construction leads to very inaccurate results since it does not take into account different many-body states having the same energy on equal footing. Here we present a fast and surprisingly simple algorithm for generating the many-body Fock basis build from many-body Fock states having the lowest non-interacting energies. The algorithm is insensitive to details of the distribution of single-particle energies and it can be used for an arbitrary number of particles obeying bosonic or fermionic statistics. Moreover, it can be easily generalized to a larger number of components. Taking as a simple example the system of two ultra-cold bosons in an anharmonic trap, we show that exact calculations in the basis generated with the algorithm are substantially more accurate than calculations performed within the standard approach.
Tobias Dornheim, Simon Groth, Alexei Filinov
et al.
Being motivated by the surge of fermionic quantum Monte Carlo simulations at finite temperature, we present a detailed analysis of the permutation-cycle properties of path integral Monte Carlo (PIMC) simulations of degenerate electrons. Particular emphasis is put onto the uniform electron gas in the warm dense matter regime. We carry out PIMC simulations of up to $N=100$ electrons and investigate exchange-cycle frequencies, which are found not to follow any simple exponential law even in the case of ideal fermions due to the finite size of the simulation box. Moreover, we introduce a permutation-cycle correlation function, which allows us to analyse the joint probability to simultaneously find cycles of different lengths within a single configuration. Again, we find that finite-size effects predominate the observed behaviour. Finally, we briefly consider an inhomogeneous system, namely electrons in a $2D$ harmonic trap. We expect our results to be of interest for the further development of fermionic PIMC methods, in particular to alleviate the notorious fermion sign problem.
The mechanisms underlying cytoplasmic pH (pHi) regulation in rat thymic lymphocytes were studied using trapped fluorescein derivatives as pHi indicators. Cells that were acid-loaded with nigericin in choline+ media recovered normal pHi upon addition of extracellular Na+ (Nao+). The cytoplasmic alkalinization was accompanied by medium acidification and an increase in cellular Na+ content and was probably mediated by a Nao+/Hi+ antiport. At normal [Na+]i, Nao+/Hi+ exchange was undetectable at pHi greater than or equal to 6.9 but was markedly stimulated by internal acidification. Absolute rates of H+ efflux could be calculated from the Nao+-induced delta pHi using a buffering capacity of 25 mmol X liter-1 X pH-1, measured by titration of intact cells with NH4+. At pHi = 6.3, pHo = 7.2, and [Na+]o = 140 mM, H+ extrusion reached 10 mmol X liter-1 X min-1. Nao+/Hi+ exchange was stimulated by internal Na+ depletion and inhibited by lowering pHo and by addition of amiloride (apparent Ki = 2.5 microM). Inhibition by amiloride was competitive with respect to Nao+. Hi+ could also exchange for Lio+, but not for K+, Rb+, Cs+, or choline+. Nao+/Hi+ countertransport has an apparent 1:1 stoichiometry and is electrically silent. However, a small secondary hyperpolarization follows recovery from acid-loading in Na+ media. This hyperpolarization is amiloride- and ouabain-sensitive and probably reflects activation of the electrogenic Na+-K+ pump. At normal Nai+ values, the Nao+/Hi+ antiport of thymocytes is ideally suited for the regulation of pHi. The system can also restore [Na+]i in Na+-depleted cells. In this instance the exchanger, in combination with the considerable cytoplasmic buffering power, will operate as a [Na+]i- regulatory mechanism.