Search Results (253)

This work aims to study the dynamic behavior of a discrete-time chemostat model involving the effect of nutrient recycling, which is a common biological phenomenon usually left out in conventional models. Based on a continuous time model involving the interrelationship between bacterial population and nutrient concentration, a new system with nutrient recycling term is obtained by introducing the process of nutrient recycling from biomass. This model is subsequently transformed to a discrete form using the forward Euler approximation scheme. Existence and stability of all possible equilibria are examined using the characteristic equation. Necessary conditions for stability and bifurcations, including transcritical and flip types, have been derived. It turns out that the considered model cannot experience Neimark–Sacker bifurcation. The results indicate that the recycling parameter plays an important role in changing stability regions and can generate complex dynamics, including oscillations and chaos. Numerical simulations are used to verify the analytical results and to show transitions between different types of system behavior. The results imply that the relationship between nutrient input, bacterial proliferation, and the recycling process has an essential influence on the dynamics and improves the comprehension of discrete ecological models. Full article

This study aims to provide essential data for the optimal design of a transcritical CO₂ water-cooled heat pump system utilizing an internal heat exchanger (IHX). To investigate cycle and application characteristics, a heat pump test rig consisting of a compressor, gas cooler, expansion valve, evaporator, IHX, and liquid receiver was fabricated. All heat exchangers were counterflow, concentric dual copper tubes. System performance was evaluated by varying the IHX and evaporator outlet superheat degrees (10–30 °C and 0–20 °C, respectively) via expansion valve opening control, alongside changes in the secondary fluid inlet temperature. The experimental results indicate that optimal high-pressure conditions exist to maximize both capacity and coefficient of performance (COP) in cooling and heating modes. Furthermore, changes in the secondary fluid inlet temperatures of the evaporator and gas cooler significantly impact the COP, showing trends similar to conventional Freon-based systems. Ultimately, precise control of the expansion valve opening, using the IHX outlet superheat as a control variable, is a key factor in operating the CO₂ heat pump system near its maximum COP. Full article

Despite widespread vaccination programs, pertussis continues to pose a major public health challenge, primarily due to waning immunity, persistent transmission, and treatment delays. This study introduces an SVEITR model to explore the transmission dynamics and control strategies for pertussis. Unlike many existing pertussis models, this framework explicitly incorporates a treatment compartment alongside vaccination and recovery, allowing for a more thorough evaluation of disease control measures. The fundamental mathematical properties of the model are established, equilibrium points are derived, and the basic reproduction number ${\mathcal{R}}_0$ is calculated. Theoretical conditions for local and global stability of the equilibrium points are rigorously analyzed using eigenvalue theory, the Routh–Hurwitz criterion, the Castillo-Chavez methodology, and Lyapunov theory. Bifurcation analysis, conducted via center manifold theory, reveals a forward transcritical bifurcation at ${\mathcal{R}}_0=1$, confirming that disease eradication is possible when ${\mathcal{R}}_0<1$. Local and global sensitivity analyses identify the most influential epidemiological parameters affecting disease dynamics (i.e., transmission, vaccination, and treatment rates). Numerical simulations illustrate the effects of vaccination, transmission, and treatment rates on disease progression and delineate stable and unstable endemic regions. The findings indicate that increased vaccination coverage and prompt treatment significantly reduce disease prevalence, whereas higher transmission rates intensify outbreaks. The proposed model offers new insights into the combined effects of vaccination and treatment in controlling pertussis and provides a quantitative framework for designing effective public health intervention strategies. Full article

Persistence, coexistence, and boundary transcritical relays are usually studied through model-specific analyses in mathematical epidemiology, ecology, population dynamics, and chemical reaction network theory. Although these fields address closely related questions, they have developed largely independently. This separation is reflected, for example, in the limited mentions of the multi-strain epidemiologic models in ecology’s chemostats and gradostats literature, despite the fact that these are revealed to be very similar once the concept of siphons from chemical reaction network theory is integrated. Conversely, the next-generation matrices and invasion graphs from eco-epidemiology are not mentioned in chemical reaction network theory. Our contribution is firstly conceptual, terminological and definitional: we propose a common framework for the study of boundary phenomena in all positive ODE subfields. We introduce and formalize notions like reproduction and invasion functions attached to siphon faces, relay graphs, relay tables, and boundary transcritical relays. Some of these concepts are known in one of the above fields but largely absent from the others, while others appear to be new; taken together, they suggest a common language for the analysis of boundary phenomena in positive dynamical systems. The usefulness of the framework is illustrated on multi-strain epidemic models like the Feng–Gavish model, for which we derive explicit, testable conditions. For example, invasion of the less fit strain into the fitter strain’s equilibrium is sufficient for coexistence—unconditionally under permanent immunity and together with an explicit feasibility condition on a reduced coexistence polynomial otherwise (for this model, mutual invasibility also ensures persistence; whether invasion is also necessary for coexistence, and explicit further assumptions under which one or the other criterion works for a larger class of models, are still open). Our approach rests on four pillars: (i) Siphon (a CRN concept) geometry, namely, the fact that forward-invariant coordinate faces correspond to siphons, with the disease-free face being the intersection of minimal siphons. (ii) The recently established fact that a transversal Jacobian block on a siphon face is Metzler, which puts under spotlight the roles of its Perron eigenvectors. (iii) A bifurcation theorem linking eigenvalue crossing at a boundary transcritical invasion relay to the emergence of a positive branch on an adjacent face. (iv) Next-generation matrices (NGMs), an ME concept: on siphon faces, NGMs may be defined via regular splittings, and invasibility may be determined by comparing their spectral radii to >1. Full article

Carbon dioxide is the number one choice for use as a natural refrigerant for environmentally friendly and sustainable solutions in refrigeration technologies today. It is used for new installations required for all types of applications, from small cold rooms in restaurants or supermarkets to large industrial applications. Practically, it is used to cool down solid products or liquids. Due to its significant inefficiencies, especially related to high operating pressures and throttling processes, the basic CO₂ transcritical refrigeration system requires improvement for superior overall efficiency. For this reason, this review paper provides insight into four types of improved CO₂ transcritical refrigeration systems: first, a CO₂ transcritical refrigeration system with one EJ or dual EJs, parallel compression, and mechanical subcooling; second, a CO₂ transcritical refrigeration system with two-stage heat recovery and a GS/CC heat exchanger; third, a CO₂ transcritical refrigeration system with two-stage compression and intermediary gas supplementation; and fourth, a solar-assisted ejector subcooling CO₂ transcritical refrigeration system. These systems provide COP increases of 21.6%, 26.3%, 25%, up to 30.1%, and 3.4%, as calculated for certain conditions. This review paper explains the mathematical modulation assumptions, energy model construction, heat recovery thermodynamic principle, and conventional and advanced exergy evaluation. As a result, all four improved CO₂ transcritical systems have superior efficiency when compared with standard CO₂ transcritical systems, consuming less energy and being suitable for use in real applications. Full article

This paper investigates the local dynamics of a discrete predator–prey system incorporating an Allee effect and a Holling-IV functional response. After nondimensionalization, a positivity-preserving discrete model is obtained by the semi-discretization method. The non-negative fixed points are classified and their local stability is established. The center manifold theorem and local bifurcation theory are then used to prove two transcritical bifurcations at the boundary fixed points $E_1$ and $E_2$ and a saddle-node bifurcation at the positive critical fixed point $E^{*}$. Numerical equilibrium branch diagrams and phase portraits illustrate these local results. The possible Neimark–Sacker bifurcation at $E_3$ and flip bifurcation at $E_4$ are beyond the present scope of this study. Full article

Green hydrogen production through water electrolysis is a key pathway to the decarbonization of future energy systems. However, part of the electrical input is transformed into waste heat. In this study, alkaline, proton-exchange membrane, anion-exchange membrane, and solid oxide electrolysis systems are compared in terms of operating temperature, heat generation, heat transfer medium, and integration constraints. Reported COP values for commercial high-temperature vapour-compression heat pumps range from 2.4 to 5.8, depending on operating conditions. The heat-pump technologies reviewed include vapour-compression systems with single-stage, multistage, cascade, and transcritical configurations, together with absorption and adsorption systems, with a focus on suitable working fluids and practical limitations. The review distinguishes between direct heat recovery and heat recovery assisted by heat pumps, and it identifies two main areas of application: external supply for district heating, industrial consumers, and energy communities; and internal support for feedwater preheating, water cycle integration, and steam generation. A selection framework is proposed in which source- and sink-temperature compatibility determines thermodynamic feasibility, COP characterizes heat-pump performance, and LCoH supports techno-economic comparison. Direct heat recovery should be preferred when temperatures are compatible, while heat pumps can operate as enabling technologies when temperature upgrading is required and system-level economic and environmental performance remains advantageous. Full article

A fractional-order mathematical model is derived for mpox transmission dynamics that explicitly incorporates the influence of public awareness through a new awareness-dependent transmission function. The proposed incidence function models the reduction in disease transmission as the level of awareness increases, thereby capturing the dynamic interaction between epidemic progression and behavioral response. The model further accounts for asymptomatic infection, hospitalization, recovery, and awareness evolution using Caputo fractional derivatives to incorporate memory effects. Basic mathematical properties of the model, including positivity, boundedness, and existence of solutions, are established. The basic reproduction number, $R_0$, is derived using the next-generation matrix approach, and a sensitivity analysis is performed to identify the epidemiological parameters that most strongly influence disease transmission. Local and global stability analyses demonstrate that the disease-free equilibrium is locally and globally asymptotically stable whenever $R_0<1$, while an endemic equilibrium exists and is globally asymptotically stable when $R_0>1$ and a forward transcritical bifurcation occurs at $R_0=1$. Numerical simulations validate the analytical findings and illustrate the significant role of sustained public awareness in reducing disease transmission and mitigating epidemic outbreaks. The results obtained from the proposed model suggest that combining behavioral awareness strategies with conventional public health interventions can substantially improve the long-term control of mpox. Full article

Persistence, coexistence, competitive exclusion, and global asymptotic stability (GAS) are closely related problems in mathematical epidemiology that are often treated by model-specific arguments. We develop a unified approach to GAS based on Perron–Volterra Lyapunov functions $L_p$, for multi-strain epidemic reaction networks. For bilinear m-strain models with irreducible rank-one infection blocks and block-diagonal next-generation structure, these functions yield a generic competitive-exclusion partition of parameter space into at most $m+1$ regions: either the disease free equilibrium is GAS, or exactly one dominant strain persists and its boundary endemic equilibrium is GAS; see non-generic tie surfaces on which the corresponding reproduction numbers coincide. We also prove a second complete GAS partition, for two-strain models with increasing concave incidence and scalar, non-interacting strain blocks, extending the Rahman–Zou result beyond rational saturating incidence. In this class, the disease-free, single-strain, and coexistence equilibria may all occur, and explicit Lyapunov functions provide the full exclusion/coexistence partition among the four possible equilibrium supports. The construction combines five ingredients: siphons, which determine forward-invariant boundary faces; triangular Jacobian structure on siphon faces; the Metzler property of transversal Jacobians and their Perron eigenvectors; regular next-generation splittings, whose spectral radii determine invasibility; and boundary transcritical invasion relays linking eigenvalue crossings to the emergence of equilibria on adjacent faces. The resulting Perron–Volterra functions combine Volterra entropy terms for resident variables with Perron-weighted linear functionals for absent strain blocks. These constructions are implemented in the Mathematica package EpidCRN, which computes siphons, transversal blocks, invasion data, Perron weights, and candidate Lyapunov functions. For the two model classes considered here, these candidates are proved to be genuine Lyapunov functions and yield complete generic GAS partitions. Full article

Long-duration energy storage (ES) has aroused widespread concern by virtue of its potential in renewable energy consumption and the achievement of carbon neutrality goals. Compressed Carbon Dioxide Energy Storage (CCES) works as one of the most attractive technologies for long-duration ES. However, efficient and economical CCES systems are still lacking. In the present study, two novel CCES systems have been proposed, namely Closed-CCES and Semi-open-CCES. Under typical design conditions, the Closed-CCES system achieves a cycle efficiency of 62.25%, whereas the Semi-open-CCES system, featuring simultaneous cooling, heating, and power outputs, attains a superior energy storage density (ESD) of 7.38 × 10⁷ J·m⁻³. Compared with comparable energy storage systems, the two proposed systems exhibit distinct advantages in cycle efficiency and energy storage density, respectively. As noted by exergy analysis, the key loss source of Closed-CCES is the heat exchanger HE2, while the loss of Semi-open-CCES is mainly concentrated in the thermal storage device HFT1. Sensitivity analysis shows that ambient temperature and thermal storage pressure slightly affect the performance of both systems, while heat exchanger efficiency impacts the performance of Closed-CCES more significantly. Economic assessments reveal that both systems outperform conventional technologies in levelized cost of electricity (LCOE). The Closed-CCES system demonstrates superior economic viability with a lower LCOE of 0.0808 $/kW·h versus 0.0985 $/kW·h for the Semi-open system, with the advantage persisting in various operational scenarios. Research results provide a basis for the practical engineering implementation of CCES technology, contributing to the broader pursuit of long-duration energy storage solutions for carbon neutrality. Full article

This investigation introduces a conceptual configuration for an innovative combined cooling and power (CCP) arrangement that harnesses waste thermal energy from a supercritical carbon dioxide (sCO₂) power loop through integration with a cascading transcritical CO₂ cycle coupled with a lithium bromide–water vapor absorption chiller (tCO₂/LiBr-H₂O VAR). A systematic comparative assessment of thermodynamic behavior and exergoeconomic characteristics was executed across three configurations: the newly proposed CCP scheme, a hybrid sCO₂/tCO₂ power system, and a conventional standalone sCO₂ engine. Parametric sensitivity analyses were conducted to evaluate how various operating parameters influence overall system effectiveness, while particle swarm optimization (PSO) was employed to determine the optimal exergetic efficiency peaks and minimum unit product costs for each architecture. Findings demonstrate that the proposed CCP topology delivers exergy efficiency enhancements of 8.46% and 1.65% relative to the standalone sCO₂ configuration and the combined sCO₂/tCO₂ arrangement, respectively. Correspondingly, reductions in total product unit costs reach 2.80% and 0.80% for the same comparisons. These outcomes confirm that employing a cascading tCO₂/LiBr-H₂O VAR subsystem as the bottoming cycle represents a compelling solution for cooling and power production. Full article

High-temperature heat pumps are a promising pathway for electrifying industrial process heat, but their application to large-temperature-glide duties remains technically challenging. Milk powder spray drying is one such application, requiring air heating to approximately 200 °C while offering only low-to-medium-temperature waste heat sources. Transcritical CO₂ heat pumps are attractive for this duty because the sensible cooling profile of supercritical CO₂ can be matched to the large temperature glide of air heating. However, the high operating pressures required in transcritical CO₂ cycles lead to substantial expansion losses, creating a potential opportunity for expansion work recovery. This study evaluates ejector- and expander-based expansion work recovery in high-temperature transcritical–transcritical CO₂ heat pump cycles for spray dryer air heating. Baseline and modified cycle configurations were modelled using steady-state thermodynamic analysis and compared using heating coefficient of performance, maximum achievable sink temperature, component-level exergy destruction, and discharge-pressure sensitivity. Under the investigated conditions and assumed component efficiencies, expanders improved the COP of all evaluated cycles. TTX-2 achieved a COP of 2.35, 5.4% above its corresponding TT-2 baseline. TT-2 and the external benchmark TT-4 each achieved a COP of 2.23 at 150 bar for the investigated duty. The comparison with TT-4 is a benchmark comparison, not an evaluation of a TT-4 recovery variant. The improvement was modest, and an upper-bound break-even expander cost of approximately 150 EUR/kW of delivered heat was estimated for the most favourable expander case. Ejector cycles reduced expansion losses in some cases but did not provide a clear cycle-level COP improvement because they altered compressor pressure ratios, gas-cooler outlet conditions, and cascade heat transfer performance. These findings apply to the investigated spray dryer duty and demonstrate that reducing expansion exergy destruction alone is insufficient to guarantee improved whole-cycle performance under the stated operating and component-efficiency assumptions. Full article

Laminar counterflow multi-branch flames provide a canonical configuration for investigating interactions between oxidizer-rich and fuel-rich streams in liquid-oxygen/methane combustion systems. This study numerically investigates their flame structure and stability under transcritical conditions, with stability characterized by the extinction strain rate. Ideal-fluid (IF), partial real-fluid (PRF), and real-fluid (RF) models are compared to distinguish the effects of real-fluid thermodynamics and high-pressure transport corrections. The multi-branch flame comprises two premixed branches coupled with a central diffusion branch. Heat release from the premixed branches creates high-temperature plateaus that preheat the stagnation-region mixture and sustain the diffusion branch. Although the three models predict similar flame topologies, the IF model gives an extinction strain rate of $3.306\times {10}^6{\mathrm{s}}^{-1}$, whereas both PRF and RF predict $3.256\times {10}^6{\mathrm{s}}^{-1}$. Thus, the ideal-fluid treatment slightly overpredicts the extinction limit under the present reference condition, while high-pressure transport corrections influence the ignition location, peak temperature, and thermal diffusivity. Increasing pressure from 10 MPa to 40 MPa raises the extinction strain rate from $9.336\times {10}^5{\mathrm{s}}^{-1}$ to $4.867\times {10}^6{\mathrm{s}}^{-1}$ by strengthening heat release and reducing thermal diffusion from the high-temperature region. Oxidizer preheating markedly enhances flame stability, whereas fuel preheating has a weak effect. These findings establish the connection between real-fluid thermodynamics, branch interaction, and extinction stability, providing a physical basis for model selection, operating-condition optimization, and stability-margin assessment in transcritical liquid-oxygen/methane combustion systems. Full article

Sustainable aviation fuel is among the most practical near-term routes for aviation decarbonization because it can be used in existing aircraft, engines, and airport fuel systems with limited infrastructure changes while minimizing disruption to the aviation fuel supply chain. This review examines SAF applications in aerospace propulsion systems, focusing on production pathways, aero-engine compatibility, property prediction, and fuel heat sink potential. It compares hydroprocessed esters and fatty acids (HEFA), Fischer–Tropsch (FT), alcohol-to-jet (ATJ), synthesized iso-paraffins (SIP), and power-to-liquid (PtL) fuels in terms of feedstock type, process complexity, product composition, and blending constraints. It also assesses how molecular composition governs density, cold-flow behavior, thermal stability, coking propensity, seal compatibility, and emissions. Recent advances in molecular dynamics, machine learning, spectroscopic analysis, and uncertainty quantification show a shift from empirical estimation toward composition-based prediction, prescreening, and fuel design. For high-thermal-load propulsion systems, SAF is further evaluated as a fuel heat sink in active regenerative cooling. Current evidence points to advantages in thermal stability and low coking tendency, but important gaps remain in transcritical and supercritical heat transfer, pyrolytic heat absorption, wall-material effects, coke deposition, and heat sink capacity modeling across wide operating ranges. Full article

Carbon dioxide (CO₂/R744) is a natural refrigerant that has been widely studied as a replacement for conventional hydrofluorocarbon-based refrigerants in HVAC&R systems. However, the performance of CO₂ heat pumps depends strongly on the system architecture, component parameters, operating conditions, and pressure control. This study examines a CO₂-based heat pump integrated into an AHU with two-stage heat recovery. Heat recovery from the exhaust air is initially performed using a regenerative sorption wheel and then in an R744 heat pump with fin-and-tube heat exchangers located directly in the airflows. The operating performance of the heat pump was evaluated through system-level simulation based on commercially available component data and iterative balancing of the refrigeration cycle and air-side processes. For the investigated configuration and selected components, the proposed R744 system is compared with a conventional R410A-based reference system under the same air-side boundary conditions. Therefore, this comparison is interpreted as a system-level benchmark rather than an isolated effect of the refrigerant itself, since performance depends on the refrigerant’s properties, compressor performance, heat exchanger configuration, system architecture, and the operating limitations of the components. Simulations are performed for both heating and cooling modes, while preliminary experimental measurements from a physical prototype are presented for qualitative comparison with the simulated heating-mode trend. Full article