Simple Systems Research Articles

Photo‐Induced Active Ion Transport‐Assisted Efficient Ionic Power Harvesting from Bioinspired Janus Dual‐Field Heterostructures

AbstractNatural organisms have developed various biological ion channels/transporters to maintain normal life activities to adapt to changing environments. Significantly, ion transporters with active ion transport property show much more controllability on these activities due to a variety of external stimuli, giving guidance to construct artificial counterparts for overcoming the issues in simple nanofluidic systems restricted by self‐diffusive ion transport. Herein, a 2D nanofluidic system based on a Janus membrane (i.e., JM) is constructed, which can achieve light‐driven active ion transport and do favor for ionic power harvesting in electrolyte systems with equal concentrations. The JM is obtained through sequentially assembled montmorillonite (MMT) decorated with photoelectric molecules (i.e., PMMT) and MXene nanosheets. Due to the formed intramembrane electric field and temperature gradient caused by the efficient charge separation and localized thermal excitation under light illumination, a photovoltaic‐driven force and thermo‐osmotic are generated for preferential ion transport. In addition, the unidirectional active transport is employed to harvest ionic power, showing an output power density of 2.0 mW m−2 and a high‐performance energy conversion efficiency of 8.3 × 10−4%. The effects of the light intensity, electrolyte concentration and species on energy conversion performance are investigated, showing the university for ionic power harvesting.

Real-space decomposition of p-wave Kitaev chain

We propose an extended Bogoliubov transformation in real space for spinless fermions, based on which a class of Kitaev chains of length 2N with zero chemical potential can be mapped to two independent Kitaev chains of length N. It provides an alternative way to investigate a complicated system from the result of relatively simple systems. We demonstrate the implications of this decomposition by a Su–Schrieffer–Heeger Kitaev model, which supports rich quantum phases. The features of the system, including the groundstate topology and nonequilibrium dynamics, can be revealed directly from that of sub-Kitaev chains. Based on this connection, two types of Bardeen–Cooper–Schrieffer (BCS)-pair order parameters are introduced to characterize the phase diagram, showing the ingredient of two different BCS pairing modes. Analytical analysis and numerical simulations show that the real-space decomposition for the ground state still holds true approximately in presence of finite chemical potential in the gapful regions.

Safety risk assessment model of a subway tunnel collapse system based on improved DOW-FFTA method

Abstract Green construction considers factors such as quality, safety, efficiency, environmental protection and ecology. Under the premise of balancing basic construction capacity and green construction, prioritizing construction safety requirements and exploring the risk assessment system for the green construction of subway projects is crucial. Traditional risk assessment methods in the study of local system risks have been mostly applied to simple systems; thus, risk identification and assessment methods lack universality. The questions of how to change the existing structure of the system safety risk assessment model and establish a realistic modeling approach, as well as implement dynamic risk supervision, have become urgent problems. Here, we investigated the event risk point and proposed an integrated evaluation method of inherent, initial and real risks based on system attributes. The improved DOW chemical method was used to solve the static inherent risk severity index, and fuzzy fault tree analysis (FFTA) was used to judge the probability of out-of-control local state management. Considering the abnormal situation and the emergence of new risk information, a dynamic correction model was proposed. Finally, a static risk assessment model was established in line with the actual state of the system with local management and realistic risk assessment models that could modify the initial risk over time.

Application of Mass Service Theory to Economic Systems Optimization Problems—A Review

An interdisciplinary approach to management allows for the integration of knowledge and tools of different fields of science into a unified methodology in order to improve the efficiency of resource management of different kinds of systems. In the conditions of global transformations, it is economic systems that have been significantly affected by external destabilizing factors. This determines the focus of attention on the need to develop tools for the modeling and optimization of economic systems, both in terms of organizational structure and in the context of resource management. The purpose of this review study is to identify the current gaps (shortcomings) in the scientific literature devoted to the issues of the modeling and optimization of economic systems using the tools of mass service theory. This article presents a critical analysis of approaches for the formulation of provisions on mass service systems in the context of resource management. On the one hand, modern works are characterized by the inclusion of an extensive number of random factors that determine the performance and efficiency of economic systems: the probability of delays and interruptions in mobile networks; the integration of order, inventory, and production management processes; the cost estimation of multi-server system operation; and randomness factors, customer activity, and resource constraints, among others. On the other hand, controversial points are identified. The analytical study carried out allows us to state that the prevailing majority of mass service models applied in relation to economic systems and resource supply optimization are devoted to Markov chain modeling. In terms of the chronology of the problems studied, there is a marked transition from modeling simple systems to complex mass service networks. In addition, we conclude that the complex architecture of modern economic systems opens up a wide research field for finding a methodology for assessing the dependence of the enterprise performance on the effect of optimization provided by using the provisions of mass service theory. This statement can be the basis for future research.

A thermodynamic study of the influence of the Al2O3 content on the CaO-SiO2-YO1.5 system

In aircraft engines applications, the interactions between rare earth silicates (mainly yttrium silicates) used as Environmental Barrier Coatings (EBCs) on turbine blades and liquid calcium-magnesium-aluminosilicates (CMAS) due to the particles ingested by the engines may lead to severe damages at high temperature. Due to the large range of composition of CMAS, simplified model systems must be used to have a good comprehension of the thermochemical phenomena leading to degradation. The interaction between ceramics and CMAS can lead to the precipitation of phases as apatite Ca2Y8(SiO4)6O2 and cyclosilicate Ca3Y2(Si3O9)2 which might provide protection to the EBC. However, their thermodynamic stability depends on many parameters. In the present work, the influence of alumina Al2O3 addition to the ternary system CaO-SiO2-YO1.5 has been studied in order to verify the equilibrium with the liquid field at 1300 °C.

Self-Assembling Polypeptides in Complex Coacervation.

Intracellular compartmentalization plays a pivotal role in cellular function, with membrane-bound organelles and membrane-less biomolecular "condensates" playing key roles. These condensates, formed through liquid-liquid phase separation (LLPS), enable selective compartmentalization without the barrier of a lipid bilayer, thereby facilitating rapid formation and dissolution in response to stimuli. Intrinsically disordered proteins (IDPs) or proteins with intrinsically disordered regions (IDRs), which are often rich in charged and polar amino acid sequences, scaffold many condensates, often in conjunction with RNA.Comprehending the impact of IDP/IDR sequences on phase separation poses a challenge due to the extensive chemical diversity resulting from the myriad amino acids and post-translational modifications. To tackle this hurdle, one approach has been to investigate LLPS in simplified polypeptide systems, which offer a narrower scope within the chemical space for exploration. This strategy is supported by studies that have demonstrated how IDP function can largely be understood based on general chemical features, such as clusters or patterns of charged amino acids, rather than residue-level effects, and the ways in which these kinds of motifs give rise to an ensemble of conformations.Our laboratory has utilized complex coacervates assembled from oppositely charged polypeptides as a simplified material analogue to the complexity of liquid-liquid phase separated biological condensates. Complex coacervation is an associative LLPS that occurs due to the electrostatic complexation of oppositely charged macro-ions. This process is believed to be driven by the entropic gains resulting from the release of bound counterions and the reorganization of water upon complex formation. Apart from their direct applicability to IDPs, polypeptides also serve as excellent model polymers for investigating molecular interactions due to the wide range of available side-chain functionalities and the capacity to finely regulate their sequence, thus enabling precise control over interactions with guest molecules.Here, we discuss fundamental studies examining how charge patterning, hydrophobicity, chirality, and architecture affect the phase separation of polypeptide-based complex coacervates. These efforts have leveraged a combination of experimental and computational approaches that provide insight into molecular level interactions. We also examine how these parameters affect the ability of complex coacervates to incorporate globular proteins and viruses. These efforts couple directly with our fundamental studies into coacervate formation, as such "guest" molecules should not be considered as experiencing simple encapsulation and are instead active participants in the electrostatic assembly of coacervate materials. Interestingly, we observed trends in the incorporation of proteins and viruses into coacervates formed using different chain length polypeptides that are not well explained by simple electrostatic arguments and may be the result of more complex interactions between globular and polymeric species. Additionally, we describe experimental evidence supporting the potential for complex coacervates to improve the thermal stability of embedded biomolecules, such as viral vaccines.Ultimately, peptide-based coacervates have the potential to help unravel the physics behind biological condensates, while paving the way for innovative methods in compartmentalization, purification, and biomolecule stabilization. These advancements could have implications spanning medicine to biocatalysis.

Short-range order and chemical compositions of glasses along the basaltic-rhyolite sub-alkaline join by Raman and FTIR spectroscopies

Six sub-alkaline glasses with compositions progressively shifting from the tholeiitic basalt (B100) end-member to the rhyolite (R100) end-member were investigated and analysed in the same frequency domain by both Raman and FTIR. This approach highlights spectroscopic similarities and differences such as positions, widths and intensities of Raman and FTIR bands, which may also exhibit significant overlapping. Both the Raman and FTIR spectra show several peaks grouped in three main vibrational windows: 200–650 (low frequency region, named F-I in this study), 650–850 (intermediate region, F-II) and 850–1250 cm−1 (high-frequency region, F-III). In line with previous investigations, the F-I interval can be ascribed to vibrational modes involving rings of tetrahedrally coordinated cations linked by bridging oxygens. It can be fitted with three components, whereas F-II involves the motion of Si atoms within its oxygen cage and is adequately represented by two components. Finally, F-III contains different T-O (T = tetrahedrally coordinated network-forming cation) stretching bands that can be tied to the overall degree of polymerization of the glass and are fitted with four components. In some glasses, the three and the two components within F-I and F-II are identifiable in both Raman and FTIR spectra; in cases of strong peak overlap, these peaks can be complementary to one another towards our interpretation of the molecular arrangement(s) in these glasses. Indeed, the positions of the four components in F-III are first constrained in the Raman spectra, which are more identifiable, then further refined using available Raman spectra for corresponding chemically simple silicate systems. The nine fitted components can reproduce the Raman and FTIR spectra extremely well.As a function of the amount of SiO2, the positions and intensities of the three low frequency components progressively shift in both Raman and FTIR. Similarly, the two bands in the F-II intermediate region exhibit a monotonic shifting of their positions. Indeed, the components at high frequency display less significant shifting of their positions as a function of SiO2, while their intensities change more markedly in the Raman spectrum compared to those for FTIR. The vibrational components measured in this study provide a referenced dataset of assignations of the most abundant natural volcanic glasses. Therefore, it provides a diagnostic tool based on the cross-validation of Raman and FTIR spectra to quickly identify the glass chemistry, offering the possibility to expand the applicability of remote investigations.

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions.

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained (CG) approaches in k-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher order contributions. We propose a systematic framework for constructing a faithful Fourier-space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular CG models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parameterization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems.

Aggregation-Induced Fluorescence Upconversion of Pyrene under Low Fluence: In Solutions and Polymeric Nanoparticles.

In this study, aggregation-induced photon upconversion (iPUC) is demonstrated in the small polyaromatic molecule, pyrene. In binary-solvent mixtures, water, which induces the aggregation of polyaromatic molecules, assisted in triplet-triplet annihilation-based upconversion. No upconverted emission was observed in a dry solvent. Although upconverted emission in the absence of a triplet sensitizer was assigned to pyrene-aggregate-induced sensitization, the presence of a triplet sensitizer enhanced the upconversion efficiency. This experimental finding was further simulated to explore the possibility of iPUC in the condensed-phase polymer matrix. We studied 2-aminoethyl methacrylate hydrochloride-polystyrene copolymer nanoparticles embedded with the molecular upconversion system. The nanoparticle iPUC agreed with the proposition that water domains were present in polymer nanoparticles and helped aggregate pyrene in the host polymer. Despite the low systemic upconversion efficiency, this study provides a method for achieving fluorescence upconversion in relatively simple systems.

Chemiluminescence initiated by nebulization of oxidant- and catalyst-free aqueous luminol solutions

Chemiluminescence (CL), i.e., the emission of light during chemical reactions without external optical excitation, is widely used in clinical medicine, bioassays, reporter gene assays, and bioimaging. Given the complexity of traditional CL systems, which typically contain catalysts and oxidants, one-component (i.e., luminophore-only) alternatives are urgently required. Herein, to demonstrate the feasibility of such simple systems, we realize CL by nebulizing oxidant- and catalyst-free aqueous luminol solutions and demonstrate that it originates from the oxidation of luminol by the •OH radicals spontaneously formed on the microdroplet surface. The higher intensity of this CL system compared to that observed for a reference bulk-phase CL system containing H2O2 as an oxidant and FeSO4 as a catalyst is ascribed to the high specific surface area and luminol adsorption capacity of the microdroplets, and excess hydroxide ions on their surface. Thus, this work demonstrates that microdroplets provide a favorable environment for CL reactions and paves the way for the establishment of one-component CL systems.

Experimental programme on austenitic stainless steel RHS members subjected to monotonic and cyclic bending

Stainless steel is a corrosion resistant iron alloy with great potential in structural engineering due to its excellent mechanical features, durability and aesthetic properties. Since most of the existing research has concerned the behaviour of the material, the response of individual structural members, or the performance of simple structural systems under monotonic loading, one of the challenges that remains is the evaluation of the cyclic performance of members to promote its use in seismic design and exploit the excellent ductility and strain hardening properties of this material. For this reason, an experimental programme on austenitic stainless steel Rectangular Hollow Section (RHS) specimens was carried out at the Department of Civil Engineering of the Università degli Studi di Salerno in collaboration with the Universitat Politècnica de Catalunya. A total of eight RHS specimens were tested around the minor axis under both monotonic (three specimens) and cyclic (five specimens) loading, in an experimental set-up that followed a cantilever scheme. The main purpose of this study was to acquire information on the cyclic performance of austenitic steel structural members, focusing on the comparison between monotonic and cyclic behaviours. The outcomes of the tests included the load–displacement and the moment–rotation curves, the energy dissipation capacity, and the evaluation of the key rotation capacities of the members. The reported data are essential to enhance the still scarce research on the seismic behaviour of stainless steel structures.

Intrinsic simplicity of complex systems

Intrinsic simplicity of complex systems

Pharmaceutical impacts on aerobic granular sludge morphology and potential implications for abiotic removal

The goal of this study was to investigate abiotic pharmaceutical removal and abiotic pharmaceutical effects on aerobic granular sludge morphology. For 80 days, a pharmaceutical mixture containing approximately 150 μg/L each of diclofenac, erythromycin, and gemfibrozil was fed to an aerobic granular sludge sequencing batch reactor and granule characteristics were compared with those from a control reactor. Aqueous and solid phase pharmaceutical concentrations were monitored and staining was used to assess changes in biofilm structures. Solid phase pharmaceutical concentrations were elevated over the first 12 days of dosing; however, they then dropped, indicative of desorption. The lipid content in pharmaceutical-exposed granules declined by approximately half over the dosing period, though the relative concentrations of other key biofilm components (proteins, alpha-, and beta-polysaccharides) did not change. Batch experiments were conducted to try to find an explanation for the desorption observed, but reduced solid phase pharmaceutical concentrations could not be linked with the presence of common wastewater constituents such as ammonia or phosphate. Sorption of all three compounds was modeled best by the Henry isotherm, indicating that, even at 150 μg/L, granules’ sorption site coverage was incomplete. Altogether, this study demonstrates that simplified batch systems may not accurately represent the complex abiotic processes occurring in flow-through, biotic systems.

Comparative study of visible-light active BiOI and N,Pd-TiO2 photocatalysts: Catalytic ozonation for dye degradation

The increasing demand for clean water requires the development of simple, cheap, and efficient catalysts systems for water pollution remediation. To develop cheap yet efficient hybrid advanced oxidation processes for degradation of organic pollutants in water requires their systematic comparison under similar conditions to make informed decisions of economically feasible and sustainable systems. Visible light active single BiOI and N, Pd co-doped TiO2 were investigated for photocatalytic ozonation (PCO) for methylene blue (MB) degradation. Metal and non-metal co-doping improved morphology, band structure and active sites on the surface of TiO2 to shift its light absorption into the visible region. The degradation of MB with BiOI PCO and N,Pd-TiO2 PCO was practically similar but showed improvement of the ozonation mineralization efficiency. However, mineralization of MB on BiOI PCO surpassed that of N,Pd-TiO2 PCO due to band structure that influenced generated free radicals during the PCO processes. BiOI PCO system progressed through the existence and involvement of strongly oxidizing and non-selective hydroxyl radicals towards enhanced mineralization of dye and intermediates while N,Pd-TiO2 PCO was steered by the superoxide radical that is selective and had lower mineralization efficiency of formed intermediates despite its high initial degradation efficacy. The work demonstrated cheap and efficient visible light active semiconductors like BiOI as potential candidates for application in photocatalytic ozonation for real applications with matching activities to that of co-doped UV active semiconductors like TiO2. This work advances the use of visible light active semiconductors towards PCO based processes for environmental pollution remediation.

Modeling the near-field effect on molecular excited states using the discrete interaction model/quantum mechanical method.

Strong light-matter interactions significantly modify the optical properties of molecules in the vicinity of plasmonic metal nanoparticles. Since the dimension of the plasmonic cavity approaches that of the molecules, it is critical to explicitly describe the nanoparticle junctions. In this work, we use the discrete interaction model/quantum mechanical (DIM/QM) method to model the coupling between the plasmonic near-field and molecular excited states. DIM/QM is a combined electrodynamics/quantum mechanical model that uses an atomistic description of the nanoparticle. We extend the DIM/QM method to include the local field effects in the sum-over-state formalism of time-dependent density functional theory. As a test of the method, we study the interactions between small organic chromophores and metal nanoparticles. In particular, we examine how the inclusion of multiple electronic transitions and intermolecular interactions modify the coupling between molecules and nanoparticles. Using the sum-over-state formalism of DIM/QM, we show that two-state models break down when the plasmon excitation is detuned from the molecular excitations. To gain further insight, we compare the simple coupled-dipole model (CDM) with the DIM/QM model. We find that CDM works well for simple systems but fails when going beyond the single molecule or single nanoparticle cases. We also find that the coupling depends strongly on the site of the nanoparticle in which the chromophore couples to. Our work suggests the importance of explicitly describing the cavity to capture the atomistic level local field environment in which the molecule strongly couples to.

Lignin-functionalized cobalt for catalytic reductive degradation of organic dyes in simple and hybrid binary systems

To fulfill the unprecedented valorization approaches for lignocellulose, this work focuses on the potential of lignin-derived catalytic systems for bio-remediation, which are natural materials perceived to address the increased demand for eco-conscious catalyzed processes. A useful lignin-functionalized cobalt (Lig-Co) catalyst has been prepared, well-characterized and deployed for the catalyzed reducing decomposition of stable harmful organic pollutants such as methylene blue (MB) and methyl orange (MO), in simple and binary systems. The multifunctional character of lignin and the presence of various active sites can promote effectively loaded metal nanoparticles (NPs). Considerably, optimizing detoxification tests showed that the uncatalyzed use of NaBH4 as a reductive agent led to an incomplete reduction of organic contaminants over a long period of up to 65 min. Interestingly, Lig-Co catalyst exhibited a high reduction rate and turnover frequency of up to 99.23% and 24.12 min−1 for MB, respectively, while they reached 99.25% and 26.21 min−1 for MO at normal temperature. Kinetically quick catalytic reaction was also demonstrated for the hybrid system, in which the rate constant k was 0.175 s−1 and 0.165 s−1 for MB and MO, respectively, within a distinctly low reaction time of around 120 s. The reproducibility of the Lig-Co catalyst induces a desirable capacity to reduce stable dyes present simultaneously in the binary system, with 6 successive catalytic runs and over 80% of activity retained. Such robust findings underline the considerable interest in developing future lignin-mediated catalytic transformations and upscaling biomass-derived products, to meet the growing demand for sustainable and eco-friendly alternatives in various industries.

The Role of Tax Expenditures in Enabling Illicit Financial Flows

The role tax expenditures play in fostering or facilitating illicit financial flows has so far not been studied extensively. We provide an explorative overview of the linkages between tax expenditures and illicit financial flows in both source and recipient countries. In a second step, we focus on three kinds of mechanisms. In source countries we analyse the role of special economic zones and tax expenditures that target the extractive sector. In recipient countries we study the use of patent boxes and related mechanisms to attract intangible assets. Bilateral tax treaties, meanwhile, can act as facilitators of illicit financial flows because they provide legal devices with which to shift profits away from source countries, and add another layer of complexity to the tax system. To address the use and abuse of tax expenditures in this context, the transparency, tax certainty and simplicity of tax systems should be strengthened by any government trying to protect its tax base.

The Evolution of Feminist Revolutionary Garments Against Patriarchy in the Fourth-wave Feminist Movement

During the fourth-wave feminist movement, a great deal of variation is produced in the forms and symbolic systems of feminist revolutionary garments. The relationship between feminism and fashion is complex during the feminist revolt against patriarchy. Some individuals view fashion as an instrument of patriarchal domination through the restraint of the female body. Some arguments believe that fashion, as revolutionary garments, can be borrowed as a method and catalyst for a feminist revolution. Social media has provided a wider digital space for feminist activism, and connections and collaborations between feminists from different classes and cultures have become easy to establish. Hence, easily recognisable logos and simpler symbol systems were the main hallmarks of this phase of feminist revolutionary garments. This paper focuses on the characteristics, advantages, and reasons for the emergence of feminist revolutionary garments in the fourth wave of the feminist movement by comparison with previous feminist revolutionary garments. Disadvantages and potential crises of these garments, such as excessive consumerism, still exist. Overall, the expressive potential of these revolutionary garments remains difficult to ignore.

Research and design of an efficient adaptive drive with balancing friction coupling

Currently, research related to the automation of processes, systems and devices are of high relevance in the scientific and technical field: in the aerospace industry, robotics and electric transport technology. Successful automation of facilities and processes requires simplified control systems, and an adaptive mechanical system operates without a control system, which increases its reliability and efficiency. In particular, the creation of an efficient and reliable transmission of electric autonomous and mobile vehicles can be achieved by an adaptive mechanical drive with two degrees of freedom. Adaptation of the two-mobile system (2-DoF) is achieved by the proposed completely new type of transmission, namely the design of a stepless multi-speed drive with an additional friction coupling. The property of reliable adaptation of a two-mobile self-adjusting mechanical drive is independent adaptability to an external load with the help of a balancing friction coupling that provides a connection between the frictional moment and the relative angular velocity. The article presents a study of the interaction of the parameters of a two mobile system in order to improve the efficiency of a self-adjusting adaptive drive with a given wide range of regulation based on the use of a friction coupling.

A dynamical system approach to relaxation in glass-forming liquids.

The "classical" thermodynamic and statistical mechanical theories of Gibbs and Boltzmann are both predicated on axiomatic assumptions whose applicability is hard to ascertain. Theoretical objections and an increasing number of observed deviations from these theories have led to sustained efforts to develop an improved mathematical and physical foundation for them, and the search for appropriate extensions that are generally applicable to condensed materials at low temperatures (T) and high material densities where the assumptions of these theories start to become particularly questionable. These theoretical efforts have largely focused on minimal models of condensed material systems, such as the Fermi-Ulam-Pasta-Tsingou model, and other simplified models of condensed materials that are amenable to numerical and analytic treatments and that can serve to illuminate essential features of relaxation processes in condensed materials under conditions approaching integrable dynamics where clear departures from classical thermodynamics and dynamics can be generally expected. These studies indicate an apparently general multi-step relaxation process, corresponding to an initial "fast" relaxation process (termed the fast β-relaxation in the context of cooled liquids), followed by a longer "equipartition time", namely, the α-relaxation time τα in the context of cooled liquids. This relaxation timescale can be enormously longer than the fast β-relaxation time τβ so that τα is the primary parameter governing the rate at which the material comes into equilibrium, and thus is a natural focus of theoretical attention. Since the dynamics of these simplified dynamical systems, originally intended as simplified models of real crystalline materials exhibiting anharmonic interactions, greatly resemble the observed relaxation dynamics of both heated crystals and cooled liquids, we adapt this dynamical system approach to the practical matter of estimating relaxation times in both cooled liquids and crystals at elevated temperatures, which we identify as weakly non-integrable dynamical systems.