We investigate open problems in the dynamics of granular cratering, specifically concerning the forces acting upon the projectile and the influences of granular structure, inter-grain friction, and the rotational motion of the projectile. Computational experiments using the discrete element method were carried out to study the influence of solid projectiles on a cohesionless granular medium, varying parameters such as projectile and grain properties (diameter, density, friction, and packing fraction) for differing impact energies (within a relatively narrow spectrum). Below the projectile, a dense region developed, pushing it backward, ultimately resulting in its rebound at the end of its trajectory. Furthermore, solid friction played a considerable role in shaping the crater. In addition, this study reveals a relationship between the projectile's initial spin and the extent of penetration, and variations in the initial particle packing contribute to the range of scaling patterns observed in the literature. Ultimately, we introduce a bespoke scaling method that compressed our penetration length data, potentially unifying existing correlations. New insights into the formation of granular matter craters are offered by our findings.
In battery modeling, a single representative particle is used to discretize the electrode at the macroscopic scale within each volume. immune imbalance The physics employed here is insufficient to precisely model interparticle interactions within the electrodes. To resolve this, we design a model describing the evolution of degradation within a battery active material particle population, employing ideas from population genetics of fitness evolution. The state of the system is dependent on the health of each individual contributing particle. Incorporating particle size and heterogeneous degradation effects, which accumulate in the particles as the battery cycles, the model's fitness formulation considers different active material degradation mechanisms. The uneven progression of degradation within the active particle population, observable at the particle scale, is driven by the autocatalytic relationship between fitness and degradation. Particle-level degradations, especially those affecting smaller particles, contribute to the overall degradation of the electrode. The findings highlight a correspondence between specific particle degradation mechanisms and the distinctive capacity loss and voltage characteristics. On the other hand, certain aspects of electrode-level behavior can shed light on the relative significance of different particle-level degradation processes.
The fundamental centrality measures of betweenness (b) and degree (k) remain crucial in the categorization process for complex networks. A revelation is drawn from Barthelemy's publication in Eur. The study of nature and its laws, physics. Scale-free (SF) networks, according to J. B 38, 163 (2004)101140/epjb/e2004-00111-4, exhibit a maximal b-k exponent of 2, aligning with the structure of SF trees. This observation suggests a +1/2 scaling exponent, where and represent the scaling exponents for the distributions of degree and betweenness centrality, respectively. For some specific models and systems, this conjecture's validity was contradicted. We systematically analyze visibility graphs from correlated time series to expose cases where the conjecture concerning them is false for particular correlation strengths. The visibility graph of three models—the two-dimensional Bak-Tang-Weisenfeld (BTW) sandpile model, one-dimensional (1D) fractional Brownian motion (FBM), and the one-dimensional Levy walks—is under scrutiny. The Hurst exponent H and the step index control the last two cases. Regarding the BTW model and FBM with H05, the value demonstrates a magnitude exceeding 2, and is concurrently less than +1/2 within the context of the BTW model, upholding the validity of Barthelemy's conjecture for the Levy process. The significant fluctuations in the scaling b-k relationship, we assert, are the underlying cause of Barthelemy's conjecture's failure; this leads to the violation of the hyperscaling relation =-1/-1 and the emergence of anomalous behavior within the BTW and FBM models. A generalized degree's universal distribution function has been identified for models that share the scaling characteristics of the Barabasi-Albert network.
The efficient handling and movement of information across neurons is thought to be linked to noise-induced resonance, specifically coherence resonance (CR), similar to how adaptive rules in neural networks are mostly connected to the prevalence of spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Employing STDP and HSP, this paper explores CR in adaptive Hodgkin-Huxley neuron networks, either small-world or random. Through numerical investigation, we ascertain that the degree of CR is significantly influenced, in varying degrees, by the adjusting rate parameter P, controlling STDP, the characteristic rewiring frequency parameter F, governing HSP, and the parameters associated with network topology. Two persistent and robust forms of behavior were, in particular, noted. A decrease in P, which intensifies the lessening effect of STDP on synaptic weights, and a reduction in F, which slows the rate of synaptic swaps between neurons, will invariably produce higher CR values in both small-world and random networks, assuming an appropriate value for the synaptic time delay parameter c. Introducing a greater synaptic time delay (c) induces multiple coherence responses (MCRs)—multiple coherence peaks occurring as c changes—in small-world and random networks. This phenomenon is more substantial for reduced values of P and F.
Recent applications have benefitted from the exceptional attractiveness of liquid crystal-carbon nanotube nanocomposite systems. This paper offers a deep analysis of a nanocomposite material, encompassing functionalized and non-functionalized multi-walled carbon nanotubes embedded within a 4'-octyl-4-cyano-biphenyl liquid crystal medium. Analysis of thermodynamic principles reveals a lowering of the transition temperatures within the nanocomposites. Unlike non-functionalized multi-walled carbon nanotube dispersions, functionalized multi-walled carbon nanotube dispersions exhibit a heightened enthalpy. The optical band gap is narrower in the dispersed nanocomposites than in the pure sample. Dielectric investigations have shown a noticeable enhancement in the longitudinal permittivity component, causing a corresponding increase in the dielectric anisotropy of the dispersed nanocomposites. Discerningly, the conductivity of both dispersed nanocomposite materials was elevated by two orders of magnitude relative to the pure sample. Dispersed functionalized multi-walled carbon nanotubes in the system led to lower threshold voltage, splay elastic constant, and rotational viscosity. In the dispersed nanocomposite of nonfunctionalized multiwalled carbon nanotubes, the threshold voltage is marginally diminished, while both rotational viscosity and splay elastic constant are amplified. The liquid crystal nanocomposites' applicability in display and electro-optical systems is demonstrated by these findings, contingent upon parameter adjustments.
The behavior of Bose-Einstein condensates (BECs) in periodic potentials is fascinatingly tied to the instabilities observed in Bloch states. The lowest-energy Bloch states of BECs, present in pure nonlinear lattices, are dynamically and Landau unstable, thus compromising BEC superfluidity. Employing an out-of-phase linear lattice is proposed in this paper to stabilize them. Selleck HOpic The averaged interaction unveils the stabilization mechanism. Within BECs with mixed nonlinear and linear lattices, we further incorporate a constant interaction and analyze its influence on the instabilities of Bloch states in the lowest band.
We examine the complexity of spin systems with infinite-range interactions, specifically the Lipkin-Meshkov-Glick (LMG) model, under thermodynamic conditions. Through the derivation of exact expressions for Nielsen complexity (NC) and Fubini-Study complexity (FSC), we uncover several distinct features compared to the complexities in other recognised spin models. A time-independent LMG model, approaching a phase transition, shows a logarithmic divergence in the NC, similar to the divergence in entanglement entropy. In a time-dependent framework, it is nevertheless remarkable that this divergence gives way to a finite discontinuity, as demonstrated via the Lewis-Riesenfeld theory of time-dependent invariant operators. Quasifree spin models display a different behavior compared to the FSC of the variant LMG model. A logarithmic divergence is observed in the target (or reference) state's behavior as it approaches the separatrix. Geodesics initiated under diverse boundary conditions, as indicated by numerical analysis, demonstrate an attraction to the separatrix. In the immediate vicinity of the separatrix, a finite change in the affine parameter leads to an insignificant change in the geodesic's length. The NC of this model likewise demonstrates this same divergence.
Recently, the phase-field crystal approach has garnered significant interest due to its ability to model the atomic actions of a system over diffusive time scales. immediate loading An atomistic simulation model, derived from the cluster-activation method (CAM), is proposed here, extending its scope from discrete to continuous spaces. Utilizing interatomic interaction energies as input parameters, the continuous CAM method simulates a variety of physical phenomena within atomistic systems, covering diffusive timescales. The adaptability of the continuous CAM was explored through simulated crystal growth in an undercooled melt, homogeneous nucleation during solidification, and the formation of grain boundaries in pure metals.
Particles are limited to single-file diffusion in narrow channels, unable to pass each other during their Brownian motion. Throughout these processes, the diffusion of a tagged particle generally manifests as regular behavior at short durations, ultimately transitioning to a subdiffusive pattern at extended times.