Diffusion System Research Articles

Characterizing localization effects in an ultracold disordered Fermi gas by diffusion analysis

Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all particles are localized for finite-strength disorder, and the system can become partially diffusive. Unraveling the intricate signatures of localization from such observed diffusion is a longstanding problem. Here, we experimentally study a degenerate, spin-polarized Fermi gas in a disorder potential formed by an optical speckle pattern. We record the diffusion through the disordered potential upon release from an external confining potential. We compare different methods to analyze the resulting density distributions, including a new approach to capture particle dynamics by evaluating absorption-image statistics. Using standard observables, such as diffusion exponent and coefficient, localized fraction, or localization length, we find that some show signatures for a transition to localization above a critical disorder strength, while others show a smooth crossover to a modified diffusion regime. In laterally displaced disorder, we spatially resolve different transport regimes simultaneously, which allows us to extract the subdiffusion exponent expected for weak localization. Our work emphasizes that the transition toward localization can be investigated by closely analyzing the system's diffusion, offering ways of revealing localization effects beyond the signature of exponentially decaying density distribution. Published by the American Physical Society 2024

Experimental Investigation of the Performance of a Novel Ejector–Diffuser System with Different Supersonic Nozzle Arrays

The supersonic–supersonic ejector–diffuser system is employed to suck supersonic low-pressure and low-temperature flow into a high-pressure environment. A new design of a supersonic–supersonic ejector–diffuser was introduced to verify pressure control performance under different operating conditions and vacuum background pressure. A 1D analysis was used to predict the geometrical structure of an ejector–diffuser with a rectangular section based on the given operating conditions. Different numbers and types of nozzle plates were designed and installed on the ejector to study the realizability of avoiding or postponing the aerodynamic choking phenomenon in the mixing section. The effects of different geometrical parameters on the operating performance of the ejector–diffuser system were discussed in detail. Experimental investigation of the effects of different types of nozzle plates and the back pressures on the pressure control performance of the designed ejector–diffuser system were performed in a straight-flow wind tunnel. The results showed that the position, type and number of the nozzle plates have a significant impact on the beginning of the formation of aerodynamic choking. The geometry of the ejector and the operating conditions, especially the backpressure and inlet pressure of the ejecting stream, determined the entrainment ratio of the two supersonic streams. The experimental results showed that long nozzle-plate had a better performance in terms of maintaining pressure stability in the test section, while short a nozzle-plate had a better pressure matching performance and could maintain a higher entrainment ratio under high backpressure conditions.

Comparative study of nudged elastic band and molecular dynamics methods for diffusion kinetics in solid-state electrolytes

Abstract Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes. Computational methods, specifically nudged elastic band (NEB) and molecular dynamics (MD) methods, provide powerful tools for the design of solid-state electrolytes. The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures. However, it relies on simulations at temperatures much higher than working temperature. This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark. We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV. The calculated diffusion barrier is 0.31 eV from both methods. The diffusion coefficients at room temperature are 4.3×10-9 and 2.2×10-9 cm2/s, respectively, from the NEB and MD methods. Our results justify the reliability of the MD method, even though high temperature simulations have to be employed to overcome the limitation on simulation time.

Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems

Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems

Green technology diffusion model and simulation considering enterprise technology absorption capacity

ABSTRACT The diffusion and wide application of green technologies are important means to achieve climate change mitigation. Concerning the green technology absorption capacity and technology diffusion willingness of enterprises, this paper divided enterprises into four categories, constructed a green technology diffusion model and analysed the equilibrium point and stability of the model. Then, we studied the diffusion process and laws of green technology through simulation experiments. The results show that in the green technology diffusion system, the basic regeneration number is the key factor in determining the equilibrium state of green technology diffusion. The disease-free equilibrium point of the green technology diffusion system is globally asymptotically stable, and the endemic equilibrium point is locally asymptotically stable. In order to improve the speed and scale of green technology diffusion, it is necessary to create green technology diffusion sources through multiple channels, improve enterprise technology absorption capacity through multiple methods, and enhance enterprise green technology diffusion willingness at multiple levels.

On the speed of propagation in Turing patterns for reaction–diffusion systems

This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions, considerable attention has also been directed towards understanding spatio-temporal behaviours, particularly the propagation of patterning from localised disturbances. We analyse these waves of patterning using both the well-established marginal stability criterion and weakly nonlinear analysis with envelope equations. Both methods provide estimates for the wave speed but the latter method, in addition, approximates the wave profile and amplitude. We then compare these two approaches analytically near a bifurcation point and reveal that the marginal stability criterion yields exactly the same estimate for the wave speed as the weakly nonlinear analysis. Furthermore, we evaluate these estimates against numerical results for Schnakenberg and CDIMA (chlorine dioxide–iodine–malonic acid) kinetics. In particular, our study emphasises the importance of the characteristic speed of pattern propagation, determined by diffusion dynamics and a complex relation with the reaction kinetics in Turing systems. This speed serves as a vital parameter for comparison with experimental observations, akin to observed pattern length scales. Furthermore, more generally, our findings provide systematic methodologies for analysing transient wave properties in Turing systems, generating insight into the dynamic evolution of pattern formation.

АНАЛИЗ И ОЦЕНКА ИННОВАЦИОННЫХ КЛАСТЕРОВ В ЛИПЕЦКОЙ ОБЛАСТИ

Currently, the main goal of the country's economic policy is to increase the competitiveness of the state. One of the measures to ensure optimal competitiveness is the approval of innovation strategies at all levels - federal, regional, sectoral, corporate. At the same time, the competitiveness of modern economy - depends not only on technological achievements, inventions, knowledge production, but also on organisational changes that promote the commercialisation of scientific and technological research. In this regard, the advantages of the cluster approach are increasingly becoming one of the ways to improve the system of innovation diffusion and technology transfer. The chosen topic is important because innovation contributes to the development of regions, increasing competitiveness, strengthening economic growth points through high-tech innovation, such as innovation clusters, research centres and other forms of institutional support., The purpose of this study is to summarise the material studied, to identify opportunities for improving the territorial innovation cluster of the Lipetsk region.

Numerical study of diffusive fish farm system under time noise

In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties. The stochastic backward Euler (SBE) and stochastic Implicit finite difference (SIFD) schemes are designed for the computational results. In the mean square sense, both schemes are consistent with the underlying model and schemes are von Neumann stable. The underlying model has various equilibria points and all these points are successfully gained by the SIFD scheme. The SIFD scheme showed positive and convergent behavior for the given values of the parameter. As the underlying model is a population model and its solution can attain minimum value zero, so a solution that can attain value less than zero is not biologically possible. So, the numerical solution obtained by the stochastic backward Euler is negative and divergent solution and it is not a biological phenomenon that is useless in such dynamical systems. The graphical behaviors of the system show that external nutrient supply is the important factor that controls the dynamics of the given model. The three-dimensional results are drawn for the various choices of the parameters.

Tracer dynamics in the active random average process

We investigate the dynamics of tracer particles in the random average process (RAP), a single-file system in one dimension. In addition to the position, every particle possesses an internal spin variable σ(t) that can alternate between two values, ±1, at a constant rate γ. Physically, the value of σ(t) dictates the direction of motion of the corresponding particle and, for finite γ, every particle performs non-Markovian active dynamics. Herein, we study the effect of this non-Markovian behavior in the fluctuations and correlations of the positions of tracer particles. We analytically show that the variance of the position of a tagged particle grows sub-diffusively as ∼ζqt at large times for the quenched uniform initial conditions. While this sub-diffusive growth is identical to that of the Markovian/non-persistent RAP, the coefficient ζq is rather different and bears the signature of the persistent motion of active particles through higher-point correlations (unlike in the Markovian case). Similarly, for the annealed (steady-state) initial conditions, we find that the variance scales as ∼ζat at large times, with the coefficient ζa once again different from the non-persistent case. Although both ζ q and ζa individually depart from their Markovian counterparts, their ratio ζa/ζq is still equal to 2 , a condition observed for other diffusive single-file systems. This condition turns out to be true even in the strongly active regimes, as corroborated by extensive simulations and calculations. Finally, we study the correlation between the positions of two tagged particles in both quenched uniform and annealed initial conditions. We verify all our analytical results using extensive numerical simulations.

On the fractional-in-time Keller-Segel model via Sonine kernels

In this paper, we study the existence and asymptotic behavior to a diffusion system which is non-local in time. As consequence of our theorems we deduce new results for the fractional-in-time Keller-Segel model. Our approach is intimately related with the Sonine kernels.

Invariant Regions and Global Existence of Uniqueness Weak Solutions for Tridiagonal Reaction-Diffusion Systems

In this paper we study the existence of uniqueness global weak solutions for m × m reaction-diffusion systems for which two main properties hold: the positivity of the weak solutions and the total mass of the components are preserved with time. Moreover, we suppose that the non-linearities have critical growth with respect to the gradient. The technique we use here in order to prove global existence is in the same spirit of the method developed by Boccardo, Murat, and Puel for a single equation. Keywords: Semigroups, local weak solution, global weak solution, reaction- diffusion systems, invariant regions, matrice of diffusion.

Patterns dynamics in a diffusive prey–predator system with ratio-dependent functional response in a planar domain

This paper is concerned with a classical two-species prey–predator reaction–diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangle domain. By analyzing the associated eigenvalue problem, the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of system at the constant coexistence equilibrium are established. Then when the bifurcation parameter is in the interior of range for Turing instability and near Turing bifurcation curve, the amplitude equations of the original system near the constant coexistence equilibrium are obtained by multiple-scale time perturbation analysis. On the basis of the obtained amplitude equations, the stability and classifications of spatiotemporal patterns of the original system at the constant coexistence equilibrium are discussed. Finally, to verify the validity of the obtained theoretical results, numerical simulations are also carried out.

Global existence of solutions for the drift–diffusion system with large initial data in [formula omitted] ([formula omitted])

In this paper, we study the Cauchy problem of the drift–diffusion system arising from semiconductor model. We prove that if a certain nonlinear function of the initial data is small enough, in a Besov type space, then there is a global solution to this drift–diffusion system. We also provide an example of initial data satisfying that nonlinear smallness condition, but whose norm be chosen arbitrarily large in Ḃ∞,∞−2(Rd).

Evaluation of topological protection in kagome lattice-based thermal diffusion systems

We evaluated topological protection for edge and higher-order corner states in topological diffusion systems based on the breathing kagome lattice. In the kagome lattice, the corner states appear at the corner boundary where all three Wannier centers in nontrivial unit cells are located. The three Wannier centers in a unit cell can be placed on the obtuse- and acute-corner boundaries utilizing the armchair boundary, generating topological acute- and obtuse-corner states. For another representative zigzag boundary, only the acute-corner unit cell has three Wannier centers located at the boundary; hence, only the acute-corner state appears. Our band analysis and numerical studies show that the topologically protected decay behavior for armchair boundaries is as robust as that for zigzag boundaries, unlike wave phenomena with space and time periodicities. Our findings can guide the flexible design of topological diffusion applications such as heat localization and recovery systems.

Kardar-Parisi-Zhang universality in two-component driven diffusive models: Symmetry and renormalization group perspectives.

We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations. We thus establish that these models belong to the 1D KPZ universality class.

Stability analysis of the stochastic Grey‐Scott model using spectral method

The Grey‐Scott model is a prominent reaction–diffusion system that has sustain consequential recent research about patterning creation in the reaction–diffusion systems. The present research work, explore the stability analysis of a proposed stochastic Grey‐Scott model, which recommend the randomness or unpredictability into the complex system. To take into account the different variations in reactant concentrations profiles, the stochasticity is modeled using the additive white noise terms. To investigate the stability characteristics of the stochastic Grey‐Scott model, we use the spectral collocation technique. Such mathematical perspective sheds light on the different system's behavior in the addition of white noise, and also it may have significance for comprehending processes in the real world that are controlled by comparable dynamics.

Predicting the Emergence of Localised Dihedral Patterns in Models for Dryland Vegetation

Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as ‘fairy circles’. Recent results from radial spatial dynamics show that approximations of localised patterns with dihedral symmetry emerge from a Turing instability in general reaction–diffusion systems, which we apply to several vegetation models. We present a systematic guide for finding such patterns in a given reaction–diffusion model, during which we obtain four key quantities that allow us to predict the qualitative properties of our solutions with minimal analysis. We consider four well-established vegetation models and compute their key predictive quantities, observing that models which possess similar values exhibit qualitatively similar localised patterns; we then complement our results with numerical simulations of various localised states in each model. Here, localised vegetation patches emerge generically from Turing instabilities and act as transient states between uniform and patterned environments, displaying complex dynamics as they evolve over time.

State of art of hydrogen utilization for building sector and set-up with preliminary experimental results of 1 kWel solid oxide fuel cell installed in a nearly zero energy house

The diffusion on large scale of the hydrogen-fueled technologies could be a strategy for boosting the expected decarbonisation of the civil sector. However, there are still a lot of unanswered questions about the real feasibility and the problems of the integration in a pre-existing building-plants system. Despite some conflicting opinions, the research about the application of the hydrogen system in the building sector must continue to make the technology more attractive and easily available at low cost. Therefore, first of all, the paper analyses advantages and issues through a broad overview. The main limits of the available studies regard both the approach and the technology integration. Indeed, there are few data about in-field performance analysis since the simulative/numerical investigations are usually based on in-lab prototypes. The most diffused systems referred to integrated energy solutions with proton exchange membrane fuel cell technology and in any case the integration in very low energy buildings such as the nearly zero energy (nZEB) ones is not discussed. Then basing on the discussed research gap, the paper focuses on the set-up of a new installation of micro-combined cooling, heating and power unit based on solid oxide fuel cell technology fueled by green hydrogen. The complexity in the design of the integration with other innovative plant configurations is discussed considering as real case study a nZEB in Mediterranean climate. Preliminarily experimental results show that the combination of fuel cell and photovoltaic system could bring to positive energy with surplus energy, during autumn season, of about 23.8 kWh. Moreover, it is also proposed the validation of a dynamic numerical model developed by means of TRNSYS (Transient System Simulation Tool) that will be used for further sensitivity analysis.

Bifurcation analysis of a diffusive predator–prey model with fear effect

In this paper, a diffusive predator–prey system with fear factor response subject to Neumann boundary conditions is considered. Bifurcations at the boundary equilibria of the corresponding ODE are confirmed by Sotomayor's theorem. Detailed bifurcation analysis shows that the reaction–diffusion system undergoes Hopf bifurcation and steady‐state bifurcation. The bifurcation direction and the stability of the bifurcating periodic solutions are also given. Finally, numerical simulation results are carried out to verify the theoretical results.

How do productivity gradient and diffusion shape patterns in a plant–herbivore grazing system?

Natural systems show heterogeneous patchy distributions of vegetation over large landscapes. Reaction–diffusion systems can demonstrate such heterogeneity of species distributions. Here, we analyse a reaction–diffusion model of plant–herbivore interactions in two-dimensional space to illustrate non-homogeneous distributions of plants and herbivores. The non-spatial system shows bottom-up control, where herbivore density is low under low and high primary productivity but increased at intermediate productivity. In addition, the non-spatial system provides bistability between a dense vegetation state devoid of herbivores and a coexisting state of plants and herbivores. In the spatiotemporal model, we give analytical conditions of occurring diffusion-driven (Turing) instability, where a novel point in our model is the relative dispersal of herbivores, which represents the movement of herbivores from a higher to a lower vegetation state in addition to the self-diffusion of both species. It is shown that heterogeneity in the population distribution does not occur if the relative dispersal of herbivores is low, but it appears in the opposite case. Due to bistability in the underlying non-spatial system, the spatiotemporal model produces initial value-dependent patterns. The two initial values make different patterns despite having the same primary productivity and relative dispersal rate. As productivity increases with a given relative herbivore dispersal, pattern transition occurs from a blend of stripes and spots of low vegetation state to a predominantly low-density vegetation state with smaller patches of densely vegetated states with one initial value. On the contrary, a discernible change in vegetation patterns from cold spots in the dense vegetation to hot stripes in the primarily low-vegetated state is noticed under the other initial population value. Furthermore, the population distributions of plants and herbivores in the entire domain after a long period are heterogeneous for both initial values, provided the relative herbivore dispersal is substantial. We estimated mean population densities to observe species fitness in the whole domain under variable productivity. When productivity is high, the mean population density of plants may go up or down, depending on the herbivore’s relative dispersal rate. In contrast to the bottom-up control dynamics of the non-spatial system, the system exhibits a top-down control under high relative dispersal, where the herbivore regulates vegetation growth under high productivity. On the other hand, herbivores are extinct under high productivity if the relative dispersal is low.