Small System Sizes Research Articles

Phase behavior of metastable water from large-scale simulations of a quantitatively accurate model near ambient conditions: The liquid-liquid critical point.

The molecular mechanisms of water's unique anomalies are still debated upon. Experimental challenges have led to simulations suggesting a liquid-liquid (LL) phase transition, culminating in the supercooled region's LL critical point (LLCP). Computational expense, small system sizes, and the reliability of water models often limit these simulations. We adopt the CVF model, which is reliable, transferable, scalable, and efficient across a wide range of temperatures and pressures around ambient conditions. By leveraging the timescale separation between fast hydrogen bonds and slow molecular coordinates, the model allows a thorough exploration of the metastable phase diagram of liquid water. Using advanced numerical techniques to bypass dynamical slowing down, we perform finite-size scaling on larger systems than those used in previous analyses. Our study extrapolates thermodynamic behavior in the infinite-system limit, demonstrating the existence of the LLCP in the 3D Ising universality class in the low-temperature, low-pressure side of the line of temperatures of maximum density, specifically at TC = 186 ± 4 K and PC = 174 ± 14 MPa, at the end of a liquid-liquid phase separation stretching up to ∼200 MPa. These predictions align with recent experimental data and sophisticated models, highlighting that hydrogen bond cooperativity governs the LLCP and the origin of water anomalies. We also observe substantial cooperative fluctuations in the hydrogen bond network at scales larger than 10nm, even at temperatures relevant to biopreservation. These findings have significant implications for nanotechnology and biophysics, providing new insights into water's behavior under varied conditions.

Flow patterns and energy spectra in forced quasi-two-dimensional turbulence: effect of system size and damping rate

An experimental investigation is conducted to study the flow patterns, spectral properties and energy fluxes in thin-layer turbulence with varying system sizes and damping rates. It is found that although a system-size vortex (an indicator of spectral condensation) occurs for small system sizes and does not for large ones, the spectra for different system sizes consistently exhibit a scaling close to $k^{-3}$ in inverse cascade (another indicator of spectral condensation). On the other hand, under a fixed system size larger than the friction-dominated length scale, the energy spectrum in the inverse cascade range changes from $k^{-3}$ to $k^{-5/3}$ as the damping rate increases, suggesting that the friction-dominated length scale may not be a suitable parameter for predicting spectral transition. At lower damping rates and large system sizes, turbulent structures grow larger via inverse cascade, manifesting as long streamers, and the small-scale vortices are suppressed. This suppression leads to a reduction of energy flux at intermediate scales and a change in the spectral shape. The dimensionless Taylor microscale is found to exhibit a monotonic dependence on the damping rate. With the reduction in the damping rate, the Taylor microscale increases to become comparable with the forcing scale, and the spectrum in inverse cascade transits to a steeper scaling, $k^{-3}$ , indicating that the dimensionless Taylor microscale may be used as a diagnostic parameter for spectral transition.

Dissipative quantum Hopfield network: a numerical analysis

Abstract We present extensive simulations of a quantum version of the Hopfield Neural Network to explore its emergent behavior. The system is a network of $N$ qubits oscillating at a given $\Omega$ frequency and which are coupled via Lindblad jump operators built with local fields $h_i$ depending on some given stored patterns. Our simulations show the emergence of pattern-antipattern oscillations of the overlaps with the stored patterns similar (for large $\Omega$ and small temperature) to those reported within a recent mean-field description of such a system, and which are originated deterministically by the quantum term including $s_x^i$ qubit operators. However, in simulations we observe that such oscillations are stochastic due to the interplay between noise and the inherent metastability of the pattern attractors induced by quantum oscillations, and then are damped in finite systems when one averages over many quantum trajectories. In addition, we report the system behavior for large number of stored patterns at the lowest temperature we can reach in simulations (namely $T=0.005\, T_C$). Our study reveals that for small-size systems the quantum term of the Hamiltonian has a negative effect on storage capacity, decreasing the overlap with the starting memory pattern for increased values of $\Omega$ and number of stored patterns. However, it also impedes the system to be trapped for long time in mixtures and spin-glass states. Interestingly, the system also presents a range of $\Omega$ values for which, although the initial pattern is destabilized due to quantum oscillations, other patterns can be retrieved and remain stable even for many stored patterns, implying a quantum-dependent nonlinear relationship between the recall process and the number of stored patterns.

Design of Small-Size Lithium-Battery-Based Electromagnetic Induction Heating Control System

This paper presents the design and optimization of a small-size electromagnetic induction heating control system powered by a 3.7 V–900 mAh lithium battery and featuring an LC series resonant full-bridge inverter circuit, which can be used for small metal material heating applications, such as micro medical devices. The effects of the resonant capacitance, inductor wire diameter, heating tube material, and wall thickness were studied to maximize the heating rate of the workpiece and simultaneously reduce the temperature rise of the NMOS transistor. The optimal circuit configuration meeting the design requirements was finally identified by comparing the operational parameters and NMOS transistor loss under different circuit conditions. Validation experiments were conducted on designed electromagnetic induction smoking devices. The results indicate that under an output current of 4.6 A, the heating tube can reach the temperature target of 250 °C within 11 s, and all NMOS transistors stay below 50 °C in a 5 min heating process.

Complete realization of energy landscapes and non-equilibrium trapping dynamics in small spin glass and optimization problems

Energy landscapes are high-dimensional surfaces underlie all physical systems, which determine crucially the energetic and behavioral dependence of the systems on variable configurations, but are difficult to be analyzed due to their high-dimensional nature. Here we introduce an approach to reveal for the complete energy landscapes of spin glasses and Boolean satisfiability problems with a small system size, and unravels their non-equilibrium dynamics at an arbitrary temperature for an arbitrarily long time. Remarkably, our results show that it can be less likely for the system to attain ground states when temperature decreases, due to trapping in individual local minima, which ceases at a different time, leading to multiple abrupt jumps in the ground-state probability. For large systems, we introduce a variant approach to extract partially the energy landscapes and observe both semi-analytically and in simulations similar phenomena. This work introduces new methodology to unravel the energy landscapes and non-equilibrium dynamics of glassy systems, and provides us with a clear, complete and new physical picture on their long-time behaviors inaccessible by existing approaches.

Integrated on-board electric vehicle battery charger with multifunctional features

ABSTRACT Because of the continuous demand for reliable, efficient, small-size, light weighted, and low-cost Electric Vehicle (EV) battery charging systems, an integrated on-board charger is proposed with a high-power propulsion motor drive. It utilises stator windings of motor, the 6-leg Voltage Source Converter (VSC), DC-DC converter, and feedback sensors to facilitate vehicular battery charging. With this system, soft switching technique based bidirectional isolated DC-DC converter is proposed that offers the advantage of simple circuitry design due to no usage of extra passive or active components. This paper presents mathematical modelling, analysis, and controller design of this proposed configuration under various operating modes. The complete system is developed in Sim Power system toolbox of MATLAB software and tested in real-time environment. The performance investigations of proposed system are carried out for three operating modes like Grid-to-Vehicle (G2V), Vehicle-to-Grid (V2G), Vehicle-to-Vehicle (V2V) under Constant Current (CC) and Constant Voltage (CV) battery charging modes. Furthermore, the investigations ensure the system’s excellent efficiency, less THD, and nearly unity power factor operation under all operating conditions.

Engineering the Kitaev Spin Liquid in a Quantum Dot System.

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin-liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of 12 quantum dots. Despite the small system size, there are clear signatures of the Kitaev spin-liquid ground state, and there is a range of parameters where these signatures are predicted, allowing a potential platform where Kitaev spin-liquid physics can be explored experimentally in quantum dot plaquettes.

A Spectral Investigation of Criticality and Crossover Effects in Two and Three Dimensions: Short Timescales with Small Systems in Minute Random Matrices.

Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume-Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior.

Contrasting the nature of plastic fluctuations in small-sized systems of BCC and FCC materials

It is now well established that, upon decreasing system sizes down to a few μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}m or below, the nature of plasticity of metallic materials is changing. Two important features of this small-sizes plasticity are two size effects, which can be summed up as “smaller is stronger” and “smaller is wilder”, this last observation meaning that the jerkiness of plastic deformation becomes prominent at small enough system sizes. In FCC and HCP materials, this is now rather well understood within the framework of obstacle-controlled plasticity, from the key role of a scaling ratio between the system size L and an internal scale l mainly dictated by dislocation patterning in pure materials, or by the nature of extrinsic disorder in alloys. The situation is more complex in BCC materials, for which screw dislocation motion becomes lattice-controlled, i.e. is thermally activated, below a transition temperature Ta\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_a$$\\end{document}. Therefore, in small-sized BCC systems, temperature, size and strain-rate effects combine to give rise to a complex landscape. We show, from an analysis of the literature as well as micropillar compression tests on Molybdenum performed with different sample sizes, under different temperatures and different applied strain-rates, that (i) near or above Ta\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_a$$\\end{document}, the plasticity of pure BCC metals is athermal and obstacle-controlled, much like at bulk scales, therefore mimicking that of pure FCC metals; (ii) below Ta\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_a$$\\end{document} and for sample sizes larger than ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim$$\\end{document}1 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}m, BCC plasticity becomes lattice-controlled, this damping dislocation avalanches and thus reducing wildness; but (iii) for very small systems, still below Ta\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_a$$\\end{document}, the role of screw dislocations on plasticity vanishes, i.e. is no more lattice-controlled, opening again the door for wild plastic fluctuations and jerkiness.

Simulating the rheology of dense suspensions using pairwise formulation of contact, lubrication and Brownian forces

Dense suspensions of solid particles in viscous liquid are ubiquitous in both industry and nature, and there is a clear need for efficient numerical routines to simulate their rheology and microstructure. Particles of micron size present a particular challenge: at low shear rates, colloidal interactions control their dynamics while at high rates, granular-like contacts dominate. While there are established particle-based simulation schemes for large-scale non-Brownian suspensions using only pairwise lubrication and contact forces, common schemes for colloidal suspensions generally are more computationally costly and thus restricted to relatively small system sizes. Here, we present a minimal particle-based numerical model for dense colloidal suspensions that incorporates Brownian forces in pairwise form alongside contact and lubrication forces. We show that this scheme reproduces key features of dense suspension rheology near the colloidal-to-granular transition, including both shear thinning due to entropic forces at low rates and shear thickening at high rates due to contact formation. This scheme is implemented in LAMMPS, a widely used open source code for parallelised particle-based simulations, with a runtime that scales linearly with the number of particles, making it amenable for large-scale simulations.

A Hybrid Monte Carlo study of argon solidification

Abstract A GPU-based implementation of the Hybrid Monte Carlo (HMC) algorithm is presented to explore its utility in the chemistry of solidification at the example of liquid to solid argon. We validate our implementation by comparing structural characteristics of argon fluid-like phases from HMC and MD simulations. Examining solidification, both MD and HMC show similar trends. Despite observable differences, MD simulations and HMC agree within the errors during the phase transition. Introducing voids decreases the solidification temperature, aiding in the formation of a well-structured solids. Further, our findings highlight the importance of larger system sizes in simulating solidification processes. Simulations with a temperature dependent potential show ambiguous results for the solidification which may be attributed to the small system sizes. Future work aims to expand HMC capabilities for complex chemical phenomena in phase transitions.

Formation of radar frame flow in a spatially distributed system of small-size airborne radar systems

Formation of radar frame flow in a spatially distributed system of small-size airborne radar systems

Critical and tricritical singularities from small-scale Monte Carlo simulations: the Blume–Capel model in two dimensions

We show that accurate insights into the critical properties of the Blume–Capel model at two dimensions can be deduced from Monte Carlo simulations, even for small system sizes, when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins. We also show that the zeros are very sensitive to subtle crossover effects.

Design for dependability — State of the art and trends

This paper presents an overview of design for dependability as a process involving three distinct but interrelated activities: risk analysis, risk mitigation, and risk assessment. Although these activities have been the subject of numerous works, few of them address the issue of their integration into rigorous design flows. Moreover, most existing results focus on dependability for small-size safety-critical systems with specific static architectures. They cannot be applied to large systems, such as autonomous systems with dynamic heterogeneous architectures and AI components. The overwhelming complexity and lack of interpretability of AI present challenges to model-based techniques and require empirical approaches. Furthermore, it is impossible to cope with all potential risks at design time; run-time assurance techniques are necessary to cost-effectively achieve the desired degree of dependability. The paper synthesizes the state of the art showing particularly the impact of new trends stemming from the integration of AI components in design flows. It argues that these trends will have a profound impact on design methods and the level of dependability. It advocates the need for a new theoretical basis for dependability engineering that allows the integration of traditional model-based approaches and data-driven techniques in the search for trade-offs between efficiency and dependability.

Kardar-Parisi-Zhang universality in the coherence time of nonequilibrium one-dimensional quasicondensates.

We investigate the finite-size origin of the coherence time (or equivalently of its inverse, the emission linewidth) of a spatially extended, one-dimensional nonequilibrium condensate. We show that the well-known Schawlow-Townes scaling of laser theory, possibly including the Henry broadening factor, only holds for small system sizes, while in larger systems the linewidth displays a novel scaling determined by Kardar-Parisi-Zhang physics. This is shown to lead to an opposite dependence of the coherence time on the optical nonlinearity in the two cases. We then study how subuniversal properties of the phase dynamics such as the higher moments of the phase-phase correlator are affected by the finite size and discuss the relation between the field coherence and the exponential of the phase-phase correlator. We finally identify a configuration with enhanced open boundary conditions, which supports a spatially uniform steady state and facilitates experimental studies of the coherence time scaling.

Continuous input current buck DC/DC converter for small-size wind energy systems featuring current sensorless MPPT control

For decentralized electrification in remote areas, small-sized wind energy systems (WESs) are considered sustainable and affordable solution when employing an efficient, small-sized component converter integrated with a less-sophisticated, cost-effective MPPT controller. Unfortunately, using a conventional buck DC/DC converter as a MPP tracker suffer from input current discontinuity. The latter results in high ripples in the tracked rectified wind power which reduces the captured power and affects system operation especially in standalone applications which are self-sufficient and independent of grid support. Furthermore, these ripples propagate to the machine side causing vibration and torque stress which impacts turbine performance and safety. To solve this issue, a large electrolytic capacitor is placed at the buck converter input to buffer these ripples, yet at the cost of larger size, losses and reduced reliability. Oppositely, the developed C1, D4 and D6 buck converters have the merit of continuous input current at small component-size. In this paper, dynamic modelling of these three converters is developed to select the one with the least input current ripples to replace the traditional buck converter in the considered WES system. Consequently, fluctuations in the tracked power are minimized and the large buffer capacitor is eliminated. This enhances system lifetime, reduces its cost and increases tracking efficiency. Moreover, mechanical power and torque fluctuations are minimized, thus maintaining machine protection. Furthermore, a sensorless MPPT algorithm, based on converter averaged state-space model, is proposed. Being dependent on variable-step P&O algorithm, the proposed approach features simple structure, ease of control and a compromise between tracking time and accuracy besides reduced cost due to the eliminated current sensor. Simulation results verified the effectiveness of the selected converter applying the proposed MPPT approach to efficiently track the wind power under wind variations with cost-effective realization.

Signature of topology via heat transfer analysis in the Su–Schrieffer–Heeger (SSH) model

In this work, we explore how thermodynamics can be a potential tool for identifying the topological phase transition. Specifically, we focus on a one-dimensional Su–Schrieffer–Heeger (SSH) chain sandwiched between two fermionic baths. To investigate distinctive thermodynamic signatures associated with the topological phase, we employ heat flow analysis. Our results, derived using a global master equation, unveil a significant suppression of heat flow as we transition from the trivial to the topological phase. This decline in heat flow can be attributed to the reduction in transmission coefficients of non-zero energy modes within the topological phase. It may serve as an indicator of a phase transition. Furthermore, we investigate the heat flow asymmetry to search for phase transition indicators. Interestingly, no asymmetry is observed when employing fermionic baths. However, upon substituting fermionic baths with bosonic ones, we report a non-zero heat flow asymmetry. For SSH model with few fermionic sites, this asymmetry is more pronounced in the topological phase compared to the trivial phase. Therefore, the observed behavior of the heat diode provides an additional means of distinguishing between the topological and trivial phases. Finally, we delve into the contributions from both bulk and edge effects in heat flow and rectification to explore the impact of small system sizes on our findings.

ИНДИКАТИВНАЯ СОСТАВЛЯЮЩАЯ СЕБЕСТОИМОСТИ ПРОДУКТА В ПОСТРОЕНИИ МАЛОРАЗМЕРНЫХ ПРОГНОЗНЫХ ЭКОНОМИКО-МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ

The development of new methods for building smallsize systems for forecasting changes in the economic environment is a promising task. At the same time, it is necessary to use the existing experience and develop the methods of economic foresight, which in their time proved predictive power. This article considers one of the aspects of the method of leading factors, namely, the use of the price of the material used in the production of most final products as an indicator of future changes in demand. The article contains a review of the main approaches proposed in this direction, as well as an analysis of their applicability to the modern period.

ЭНЕРГЕТИЧЕСКАЯ КОМПОНЕНТА В СЕБЕСТОИМОСТИ ПРОДУКЦИИ (ПЕРСПЕКТИВЫ ИСПОЛЬЗОВАНИЯ В МАЛОРАЗМЕРНОМ ЭКОНОМИКО-МАТЕМАТИЧЕСКОМ МОДЕЛИРОВАНИИ)

The development of new methods for building small-size systems for forecasting changes in the economic environment is a promising task. At the same time, it is necessary to use the existing experience and develop the methods of economic foresight, which in their time proved predictive power. This article considers one of the aspects of the method of leading factors, namely, the use of the price of the material used in the production of most final products as an indicator of future changes in demand. The article contains a review of the main approaches proposed in this direction, as well as an analysis of their applicability to the modern period.

Rescaling invariance and anomalous energy transport in a small vertical column of grains.

It is well known that energy dissipation and finite size can deeply affect the dynamics of granular matter, often making usual hydrodynamic approaches problematic. Here we report on the experimental investigation of a small model system, made of ten beads constrained into a 1D geometry by a narrow vertical pipe and shaken at the base by a piston excited by a periodic wave. Recording the beads motion with a high frame rate camera allows to investigate in detail the microscopic dynamics and test hydrodynamic and kinetic models. Varying the energy, we explore different regimes from fully fluidized to the edge of condensation, observing good hydrodynamic behavior down to the edge of fluidization, despite the small system size. Density and temperature fields for different system energies can be collapsed by suitable space and time rescaling, and the expected constitutive equationholds very well when the particle diameter is considered. At the same time, the balance between dissipated and fed energy is not well described by commonly adopted dependence due to the up-down symmetry breaking. Our observations, supported by the measured particle velocity distributions, show a different phenomenological temperature dependence, which yields equationsolutions in agreement with experimental results.