Layered Structural PBAT Composite Foams for Efficient Electromagnetic Interference Shielding

The utilization of eco-friendly,lightweight,high-efficiency and high-absorbing electromagnetic interference(EMI)shielding composites is imperative in light of the worldwide promotion of sustainable manufacturing.In this work,magnetic poly(butyleneadipate-coterephthalate)(PBAT)microspheres were firstly synthesized via phase separation method,then PBAT composite foams with layered structure was constructed through the supercritical carbon dioxide foaming and scraping techniques.The merits of integrating ferroferric oxideloaded multi-walled carbon nanotubes(Fe3O4@MWCNTs)nanoparticles,a microcellular framework,and a highly conductive silver layer have been judiciously orchestrated within this distinctive layered configuration.Microwaves are consumed throughout the process of“absorption-reflection-reabsorption”as much as possible,which greatly declines the secondary radiation pollution.The biodegradable PBAT composite foams achieved an EMI shielding effectiveness of up to 68 dB and an absorptivity of 77%,and authenticated favorable stabilization after the tape adhesion experiment.

Micro segment analysis of supercritical methane thermal-hydraulic performance and pseudo-boiling in a PCHE straight channel

The printed circuit heat exchanger(PCHE) is receiving wide attention as a new kind of compact heat exchanger and is considered as a promising vaporizer in the LNG process. In this paper, a PCHE straight channel in the length of 500 mm is established, with a semicircular cross section in a diameter of 1.2 mm.Numerical simulation is employed to investigate the flow and heat transfer performance of supercritical methane in the channel. The pseudo-boiling theory is adopted and the liquid-like, two-phase-like, and vapor-like regimes are divided for supercritical methane to analyze the heat transfer and flow features.The results are presented in micro segment to show the local convective heat transfer coefficient and pressure drop. It shows that the convective heat transfer coefficient in segments along the channel has a significant peak feature near the pseudo-critical point and a heat transfer deterioration when the average fluid temperature in the segment is higher than the pseudo-critical point. The reason is explained with the generation of vapor-like film near the channel wall that the peak feature related to a nucleateboiling-like state and heat transfer deterioration related to a film-boiling-like state. The effects of parameters, including mass flow rate, pressure, and wall heat flux on flow and heat transfer were analyzed.In calculating of the averaged heat transfer coefficient of the whole channel, the traditional method shows significant deviation and the micro segment weighted average method is adopted. The pressure drop can mainly be affected by the mass flux and pressure and little affected by the wall heat flux. The peak of the convective heat transfer coefficient can only form at high mass flux, low wall heat flux, and near critical pressure, in which condition the nucleate-boiling-like state is easier to appear. Moreover,heat transfer deterioration will always appear, since the supercritical flow will finally develop into a filmboiling-like state. So heat transfer deterioration should be taken seriously in the design and safe operation of vaporizer PCHE. The study of this work clarified the local heat transfer and flow feature of supercritical methane in microchannel and contributed to the deep understanding of supercritical methane flow of the vaporization process in PCHE.

Demonstration of a small‐scale power generator using supercritical CO_(2)

The supercritical CO_(2)(sCO_(2))power cycle could improve efficiencies for a wide range of thermal power plants.The sCO_(2)turbine generator plays an important role in the sCO_(2)power cycle by directly converting thermal energy into mechanical work and electric power.The operation of the generator encounters challenges,including high temperature,high pressure,high rotational speed,and other engineering problems,such as leakage.Experimental studies of sCO_(2)turbines are insufficient because of the significant difficulties in turbine manufacturing and system construction.Unlike most experimental investigations that primarily focus on 100 kW‐or MW‐scale power generation systems,we consider,for the first time,a small‐scale power generator using sCO_(2).A partial admission axial turbine was designed and manufactured with a rated rotational speed of 40,000 rpm,and a CO_(2)transcritical power cycle test loop was constructed to validate the performance of our manufactured generator.A resistant gas was proposed in the constructed turbine expander to solve the leakage issue.Both dynamic and steady performances were investigated.The results indicated that a peak electric power of 11.55 kW was achieved at 29,369 rpm.The maximum total efficiency of the turbo‐generator was 58.98%,which was affected by both the turbine rotational speed and pressure ratio,according to the proposed performance map.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Multi-objective optimization and evaluation of supercritical CO_(2) Brayton cycle for nuclear power generation

The supercritical CO_(2) Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout,compact structure,and high cycle efficiency.Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy.Parametric analysis,multi-objective optimizations,and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes.Results show that for the same design thermal power scale of reactors,the higher the core’s exit temperature,the better the Brayton cycle’s thermo-economic performance.Among the four-cycle layouts,the recompression cycle(RC)has the best overall performance,followed by the simple recuperation cycle(SR)and the intercooling cycle(IC),and the worst is the reheating cycle(RH).However,RH has the lowest total cost of investment(C_(tot))of$1619.85 million,and IC has the lowest levelized cost of energy(LCOE)of 0.012$/(kWh).The nuclear Brayton cycle system’s overall performance has been improved due to optimization.The performance of the molten salt reactor combined with the intercooling cycle(MSR-IC)scheme has the greatest improvement,with the net output power(W_(net)),thermal efficiencyη_(t),and exergy efficiency(η_(e))improved by 8.58%,8.58%,and 11.21%,respectively.The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_(tot) by 27.78%.In comparison,the internal rate of return(IRR)increased by only 7.8%,which is not friendly to investors with limited funds.For the nuclear Brayton cycle,the molten salt reactor combined with the recompression cycle scheme should receive priority,and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

Control system design for a pressure-tube-type supercritical water-cooled nuclear reactor via a higher order sliding mode method

Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.

Solubility of iron(Ⅲ) and nickel(Ⅱ) acetylacetonates in supercritical carbon dioxide

As a common precursor for supercritical CO_(2)(scCO_(2))deposition techniques,solubility data of organometallic complexes in scCO_(2)is crucial for the preparation of nanocomposites.Recently,metal acetylacetonates have shown great potential for the preparation of single-atom catalytic materials.In this study,the solubilities of iron(Ⅲ)acetylacetonate(Fe(acac)3)and nickel(Ⅱ)acetylacetonate(Ni(acac)2)were measured at the temperature from 313.15 to 333.15 K and in the pressure range of 9.5–25.2 MPa to accumulate new solubility data.Solubility was measured using a static weight loss method.The semi-empirical models proposed by Chrastil and Sung et al.were used to correlate the solubility data of Fe(acac)3 and Ni(acac)2.The equations obtained can be used to predict the solubility of the same system in the experimental range.

Conventional Geothermal Systems and Unconventional Geothermal Developments: An Overview

This paper provides an overview of conventional geothermal systems and unconventional geothermal developments as a common reference is needed for discussions between energy professionals. Conventional geothermal systems have the heat, permeability and fluid, requiring only drilling down to °C, normal heat flow or decaying radiogenic granite as heat sources, and used in district heating. Medium-temperature (MT) 100°C - 190°C, and high-temperature (HT) 190°C - 374°C resources are mostly at plate boundaries, with volcanic intrusive heat source, used mostly for electricity generation. Single well capacities are °C - 500°C) and a range of depths (1 m to 20 Km), but lack permeability or fluid, thus requiring stimulations for heat extraction by conduction. HVAC is 1 - 2 m deep and shallow geothermal down to 500 m in wells, both capturing °C, with °C are either advanced by geothermal developers at <7 Km depth (Enhanced Geothermal Systems (EGS), drilling below brittle-ductile transition zones and under geothermal fields), or by the Oil & Gas industry (Advanced Geothermal Systems, heat recovery from hydrocarbon wells or reservoirs, Superhot Rock Geothermal, and millimeter-wave drilling down to 20 Km). Their primary aim is electricity generation, relying on closed-loops, but EGS uses fractures for heat exchange with earthquake risks during fracking. Unconventional approaches could be everywhere, with shallow geothermal already functional. The deeper and hotter unconventional alternatives are still experimental, overcoming costs and technological challenges to become fully commercial. Meanwhile, the conventional geothermal resources remain the most proven opportunities for investments and development.

Modeling Blood Flow in Veins of Uniform Properties (Giraffe Jugular Vein)

This paper models the giraffe’s jugular veins as a uniform collapsible tube from a rigid skull. The equations governing one-dimensional steady flow through such a tube for various conditions have been developed. The effects of inertial and inclination angles that have not been discussed previously have been included. It has been shown that different flows for a uniform tube (vein) are possible. However, this flow matches that of a jugular vein which is supercritical, and the steady solution has been given by the balance between the driving forces of gravity and the viscous resistance to the flow at the right atrium of the heart must be sub-critical for a fixed right-atrium pressure which means that an elastic jump is required to return the flow to sub-critical from the supercritical flow upstream this type of relationship gives rise to flow limitation at the same time given any right atrium fixed pressure there exists a maximum flow rate which when exceeded the boundary conditions of the flow do not hold boundary conditions at the right atrium are not satisfied hence making the steady flow impossible this mechanism of flow limitation is slightly different from the other one in that causes airways through forced expiration from the observation made it is clearly shown that there is an intravascular pressure difference with a change in height.

Carbon dioxide capture, enhanced-oil recovery and storage technology and engineering practice in Jilin Oilfield, NE China

This paper systematically presents the established technologies and field applications with respect to research and engineering practice of CO_(2) capture,enhanced oil recovery(EOR),and storage technology in Jilin Oilfield,NE China,and depicts the available series of supporting technologies across the industry chain.Through simulation calculation+pilot test+field application,the adaptability of the technology for capturing CO_(2) with different concentrations in oilfields was confirmed.The low energy-consumption,activated N-methyl diethanolamine(MDEA)decarburization technology based on a new activator was developed,and the operation mode of CO_(2) gas-phase transportation through trunk pipeline network,supercritical injection at wellhead,and produced gas-liquid separated transportation was established.According to different gas source conditions,liquid,supercritical phase,high-pressure dense phase pressurization technologies and facilities were applied to form the downhole injection processes(e.g.gas-tight tubing and coiled tubing)and supporting anti-corrosion and anti-blocking techniques.In the practice of oil displacement,the oil recovery technologies(e.g.conical water-alternating-gas injection,CO_(2) foam flooding,and high gas-oil ratio CO_(2) flooding)and produced fluid processing technologies were developed.Through numerical simulation and field tests,three kinds of CO_(2) cyclic injection technologies(i.e.direct injection,injection after separation and purification,and hybrid injection)were formed,and a 10×10^(4) m^(3)/d cyclic injection station was constructed to achieve"zero emission"of associated gas.The CO_(2) storage safety monitoring technology of carbon flux,fluid composition and carbon isotopic composition was formed.The whole-process anti-corrosion technology with anticorrosive agents supplemented by anticorrosive materials was established.An integrated demonstration area of CO_(2) capture,flooding and storage with high efficiency and low energy-consumption has been built,with a cumulative oil increment of 32×10^(4) t and a CO_(2) storage volume of 250×10^(4) t.

Anti-Melanogenesis Activity of Supercritical Carbon Dioxide Extract from Perilla frutescens Seeds

Perilla frutescens seed (PFS) oil is reported to inhibit skin photoaging;however, its effect on melanogenesis has not yet been investigated. Herein, we tested the anti-melanogenesis activity of an oil-based extract from PFS with supercritical carbon dioxide (scCO2). In a cell culture system, B16 mouse melanoma cells were treated with the PFS scCO2 extract and other samples. The PFS scCO2 extract decreased melanin production by approximately 90% in B16 mouse melanoma cells without cytotoxicity at 100 μg/mL. This effect was greater than that of the well-known melanogenesis inhibitor, kojic acid. Although a hexane-extracted PFS oil and a squeezed PFS oil also decreased melanin production in the B16 cells, the inhibitory effect of the PFS scCO2 extract was higher than both of these. Chemical analysis of the PFS scCO2 extract and squeezed PFS oil showed that almost 90% of the components of both oils were α-linolenic acid, linoleic acid, and oleic acid. Furthermore, the ratio of those three fatty acids across both samples was almost the same. When the three fatty acids were mixed in the same ratio as in the PFS scCO2 extract, the IC50 of the mixture for melanin production in B16 melanoma cells was identical to that of the PFS scCO2 extract. However, the IC50 of the squeezed PFS oil was approximately 6.6 times higher than that of the mixture. Although those fatty acids are the main inhibitory ingredients against melanin production in all of the extracts, some factor(s) in the squeezed PFS reduce their affinity with the cells. These results indicated that the PFS scCO2 extract could be a superior melanogenesis inhibitor. Although its main ingredients are probably the same as those of the squeezed PFS oil, it is necessary to extract with scCO2 for stronger anti-melanogenesis activity.

Adsorption of methane onto mudstones under supercritical conditions: Mechanisms, physical properties and thermodynamic parameters

Since the mechanisms of methane-mudstone interactions are important for estimating shale gas reserves,methane adsorption under supercritical conditions of 30 MPa pressure and 303.15,333.15,363.15 K temperatures was studied to measure the excess methane adsorption in two mudstone samples from Yanchang Formation,Ordos Basin.Excess adsorption features inflection points where the amount of adsorbed gas changes from increasing to decreasing concentrations.Three methods(fixed,slope,and freely fitted density)were applied to calculate the adsorbed-phase density(rad),which was then used to fit the measured excess adsorption.Two criteria,the goodness-of-fit and whether the fitting can obtain reasonable absolute adsorption,were applied to determine the most accurate model.Results indicated that the supercritical Dubinin-Radushkevich(SDR)model with freely fitted rad was the most reasonable model.The volume of adsorbed methane at 363.15 K is close to the micropore(d<2 nm)volume of the corresponding mudstone.Considering the actual geological conditions,the adsorbed gas should be predominantly stored in micropores.Thermodynamic parameters reveal that the methane adsorption on mudstone is a physisorption process that is jointly controlled by the heterogeneity of,and interaction forces between the methane molecule and,the rock surface.

Experimental Research on Supercritical Carbon Dioxide Fracturing of Sedimentary Rock:A Critical Review

Supercritical carbon dioxide(ScCO_(2))fracturing has great advantages and prospects in both shale gas exploitation and CO_(2)storage.This paper reviews current laboratory experimental methods and results for sedimentary rocks fractured by ScCO_(2).The breakdown pressure,fracture parameters,mineral composition,bedding plane angle and permeability are discussed.We also compare the differences between sedimentary rock and granite fractured by ScCO_(2),ultimately noting problems and suggesting solutions and strategies for the future.The analysis found that the breakdown pressure of ScCO_(2)was reduced 6.52%–52.31%compared with that of using water.ScCO_(2)tends to produce a complex fracture morphology with significantly higher permeability.When compared with water,the fracture aperture of ScCO_(2)was decreased by 4.10%–72.33%,the tortuosity of ScCO_(2)was increased by 5.41%–70.98%and the fractal dimension of ScCO_(2)was increased by 4.55%–8.41%.The breakdown pressure of sandstone is more sensitive to the nature of the fracturing fluid,but fracture aperture is less sensitive to fracturing fluid than for shale and coal.Compared with granite,the tortuosity of sedimentary rock is more sensitive to the fracturing fluid and the fracture fractal dimension is less sensitive to the fracturing fluid.Existing research shows that ScCO_(2)has the advantages of low breakdown pressure,good fracture creation and environmental protection.It is recommended that research be conducted in terms of sample terms,experimental conditions,effectiveness evaluation and theoretical derivation in order to promote the application of ScCO_(2)reformed reservoirs in the future.

Numerical simulations of supercritical carbon dioxide fracturing:A review

As an emerging waterless fracturing technology,supercritical carbon dioxide(SC-CO_(2))fracturing can reduce reservoir damage and dependence on water resources,and can also promote the reservoir stimulation and geological storage of carbon dioxide(CO_(2)).It is vital to figure out the laws in SC-CO_(2)fracturing for the large-scale field implementation of this technology.This paper reviews the numerical simulations of wellbore flow and heat transfer,fracture initiation and propagation,and proppant transport in SC-CO_(2)fracturing,including the numerical approaches and the obtained findings.It shows that the variations of wellbore temperature and pressure are complex and strongly transient.The wellhead pressure can be reduced by tubing and annulus co-injection or adding drag reducers into the fracturing fluid.Increasing the temperature of CO_(2)with wellhead heating can promote CO_(2)to reach the well bottom in the supercritical state.Compared with hydraulic fracturing,SC-CO_(2)fracturing has a lower fracture initiation pressure and can form a more complex fracture network,but the fracture width is narrower.The technology of SC-CO_(2)fracturing followed by thickened SC-CO_(2)fracturing,which combines with high injection rates and ultra-light proppants,can improve the placement effect of proppants while improving the complexity and width of fractures.The follow-up research is required to get a deeper insight into the SC-CO_(2)fracturing mechanisms and develop cost-effective drag reducers,thickeners,and ultra-light proppants.This paper can guide further research and promote the field application of SC-CO_(2)fracturing technology.

Numerical simulation of flow and heat transfer of n-decane in sub-millimeter spiral tube at supercritical pressure

The flow and heat transfer characteristics of n-decane in the sub-millimeter spiral tube(SMST) at supercritical pressure(p = 3 MPa) are studied by the RNG k-ε numerical model in this paper. The effects of various Reynolds numbers(Re) and structural parameters pitch(s) and spiral diameter(D) are analyzed.Results indicate that the average Nusselt numberNu and friction factorNu increase with an increase in Re, and decrease with an increase in D/d(tube diameter). In terms of the structural parameter s/d, it is found that as s/d increases, the Nu first increase, and then decrease. and the critical structural parameter is s/d = 4. Compared with the straight tube, the SMST can improve Nu by 34.8% at best, while it can improve Nu by 102.1% at most. In addition, a comprehensive heat transfer coefficient is applied to analyze the thermodynamic properties of SMST. With the optimal structural parameters of D/d = 6 and s/d = 4, the comprehensive heat transfer factor of supercritical pressure hydrocarbon fuel in the SMST can reach 1.074. At last, correlations of the average Nusselt number and friction factor are developed to predict the flow and heat transfer of n-decane at supercritical pressure.

Micro-mechanical properties of shale due to water/supercritical carbon dioxide-rock interaction

To investigate the impacts of water/supercritical CO_(2)-rock interaction on the micro-mechanical properties of shale,a series of high-temperature and high-pressure immersion experiments were performed on the calcareous laminated shale samples mined from the lower submember of the third member of Paleogene Shahejie Formation in the Jiyang Depression,Bohai Bay Basin.After that,grid nanoindentation tests were conducted to analyze the influence of immersion time,pressure,and temperature on micro-mechanical parameters.Experimental results show that the damage of shale caused by the water/supercritical CO_(2)-rock interaction was mainly featured by the generation of induced fractures in the clay-rich laminae.In the case of soaking with supercritical CO_(2),the aperture of induced fracture was smaller.Due to the existence of induced fractures,the statistical averages of elastic modulus and hardness both decreased.Meanwhile,compaction and stress-induced tensile fractures could be observed around the laminae.Generally,the longer the soaking time,the higher the soaking pressure and temperature,the more significant the degradation of micro-mechanical parameters is.Compared with water-rock interaction,the supercritical CO_(2)-rock interaction caused a lower degree of mechanical damage on the shale surface.Thus,supercritical CO_(2)can be used as a fracturing fluid to prevent the surface softening of induced fractures in shale reservoirs.

Theoretical and technical progress in exploration practice of the deep-water large oil fields, Santos Basin, Brazil

The history and results of petroleum exploration in the Santos Basin, Brazil are reviewed. The regularity of hydrocarbon enrichment and the key exploration technologies are summarized and analyzed using the seismic, gravity, magnetic and drilling data. It is proposed that the Santos Basin had a structural pattern of two uplifts and three depressions and the Aram-Uirapuru uplift belt controlled the hydrocarbon accumulation. It is believed that the main hydrocarbon source kitchen in the rift period controlled the hydrocarbon-enriched zones, paleo-structures controlled the scale and quality of lacustrine carbonate reservoirs, and continuous thick salt rocks controlled the hydrocarbon formation and preservation. The process and mechanism of reservoirs being transformed by CO_(2)charging were revealed. Five key exploration technologies were developed,including the variable-velocity mapping for layer-controlled facies-controlled pre-salt structures, the prediction of lacustrine carbonate reservoirs, the prediction of intrusive/effusive rock distribution, the detection of hydrocarbons in lacustrine carbonates, and the logging identification of supercritical CO_(2)fluid. These theoretical recognitions and exploration technologies have contributed to the discovery of deep-water super-large reservoirs under CNODC projects in Brazil, and will guide the further exploration of deep-water large reservoirs in the Santos Basin and other similar regions.

Mesoporous poly(ionic liquid)s with dual active sites for highly efficient CO_(2)conversion

Atmospheric CO_(2)concentrations are soaring due to the continued use of fossil fuels in energy production,an anthropogenic activity that is playing a leading role in global warming.Thus,research aimed at the capture and conversion of CO_(2)into value-added products,such as cyclic carbonates,is booming.While CO_(2)is an abundant,cheap,non-toxic,and readily accessible Cl feedstock,its thermodynamic stability necessitates the development of highly efficient catalysts that are able to promote chemical reactions under mild conditions.In this work,a novel mesoporous poly(ionic liquid)with dual active sites was synthesized through a facile method that involves co-polymerization,post-synthetic metalation,and supercritical CO_(2)drying.Due to a high density of nucleophilic and electrophilic sites,the as-prepared poly(ionic liquid),denoted as P2D-4BrBQA-Zn,offers excellent performance in a CO_(2)cycloaddition reaction using epichlorohydrin as the substrate(98.9%conversion and 96.9%selectivity).Moreover the reaction is carried out under mild,solvent-free,and additive-free conditions.Notably,P2D-4BrBQA-Zn also efficiently promotes the conversion of various other epoxide substrates into cyclic carbonates.Overall,the catalyst is found to have excellent substrate compatibility,stability,and recyclability.

Optimization of Supercritical Extraction Process of Laoshan Black Tea by Response Surface Methodology

[Objectives]Laoshan black tea was subjected to supercritical CO_(2) extraction. [Methods]The extraction conditions of Laoshan black tea were studied by an orthogonal experiment and optimized by response surface methodology. [Results] The optimum extraction conditions of black tea extract by supercritical CO_(2) extraction were as follows: extraction pressure 23.53 MPa, extraction time 1.73 h, and extraction temperature 49.75 ℃, with which the extract yield could reach 5.15% theoretically. [Conclusions] Based on the traditional extraction process, a supercritical extraction method optimized by response surface methodology and a unique extraction process were formed, which enriches the extraction processes and methods of natural raw materials.

Existence of Supercritical Hopf Bifurcation on a Type-Lorenz System

In this paper, a system of Lorenz-type ordinary differential equations is considered and, under some assumptions about the parameter space, the presence of the supercritical non-degenerate Hopf bifurcation is demonstrated. The technical tool used consists of the Central Manifold theorem, a well-known formula to calculate the Lyapunov coefficient and Hopf’s Theorem. For particular values of the parameters in the parameter space established in the main result of this work, a graph is presented that describes the evolution of the trajectories, obtained by means of numerical simulation.