Linear Flow Research Articles

Group Cohesion and Necessary Adaptations in Online Hearing Voices Peer Support Groups: Qualitative Study With Group Facilitators.

Face-to-face hearing voices peer support groups (HVGs), a survivor-led initiative that enables individuals who hear voices to engage with the support of peers, have a long-standing history in community settings. HVGs are premised on the notion that forming authentic, mutual relationships enables the exploration of one's voice hearing experiences and, in turn, reduces subjective distress. As such, group cohesion is assumed to be a central mechanism of change in HVGs. The rise of digital mental health support, coupled with the COVID-19 pandemic, has resulted in many HVGs adapting to online delivery. However, to date no studies have examined the implementation of these online groups and the adaptations necessary to foster cohesion. This study aims to understand the experience of group cohesion among HVG facilitators in online groups compared with face-to-face groups. Specifically, we examined the ways in which the medium through which groups run (online or face-to-face) impacts group cohesion and how facilitators adapted HVGs to foster group cohesion online. Semistructured qualitative interviews were conducted with 11 facilitators with varied experience of facilitating online and face-to-face HVGs. Data were analyzed using reflexive thematic analysis. The findings are organized into 3 themes and associated subthemes: nonverbal challenges to cohesion (lack of differentiation, transitional space, inability to see the whole picture, and expressions of empathy); discursive challenges to cohesion (topic-based conversation and depth of disclosure); and necessary adaptations for online groups (fostering shared experience and using the unique context to demonstrate investment in others). Despite challenges in both the setting and content of online groups, facilitators felt that group cohesion was still possible to achieve online but that it had to be facilitated intentionally. This study is the first to specifically investigate group cohesion in online HVGs. Participants noted numerous challenges to group cohesion when adapting groups to run online, including the unnaturally linear narrative flow of dialogue in online settings; lack of transitional spaces, and associated small talk before and after the session; ease of disengagement online; inhibited sharing; and absence of shared physical presence online. Although these challenges were significant, facilitators nevertheless emphasized that the benefits provided by the accessibility of online groups outweighed these challenges. Necessary adaptations for cultivating group cohesion online are outlined and include capitalizing on moments of humor and spontaneity, using group activities, encouraging information sharing between participants using the chat and screen-sharing features, and using objects from participants' environments to gain deeper insight into their subjective worlds.

Ciliary propulsion through non-uniform flows

The classical paper by Lighthill (Commun. Pure Appl. Maths, vol. 109, 1952, p. 118) on the propulsion of ciliated microorganisms has become the reference against which many modern studies on swimming in low Reynolds number are compared. However, Lighthill's study was limited to propulsion in a uniform flow, whereas several biologically relevant microorganisms experience non-uniform flows. Here we propose a benchmark for ciliary propulsion in paraboloidal flows. We first consider the axisymmetric problem, with the microorganisms on the centreline of the background flow, and derive exact analytical solutions for the flow field. Our results reveal flow features, swimming characteristics and performance metrics markedly different from those generated in a uniform flow. In particular, the background paraboloidal flow introduces a Stokes quadrupole singularity at the leading-order flow field, generating vortices. Moreover, we determine the necessary conditions on the strength of the background flow for optimal power dissipation and swimming efficiency. We then consider the more general case of a microorganism off the centreline of the background flow. In this case, the squirmer experiences a paraboloidal, linear shear and uniform flows due to its position relative to the flow's centreline. Our findings show that while the linear shear flow does not affect the translational and rotational velocities of the squirmer, it does influence the velocity field and, therefore, the power dissipation.

An online updated linear power flow model based on regression learning

AbstractThe linear power flow (LPF) model is widely used in the optimization, operation, and control of distribution networks. These applications require the LPF model to be accurate, fast, and simple in order to simplify calculations as well as to efficiently perform operations and scheduling. In addition, it is difficult to realize the online update of parameters in the existing LPF models. The model retraining brings serious data burden and inefficiency. To serve these applications and comply with requirements, a brand new LPF model is proposed in this paper. A quadratic power flow model is trained by regression learning first, and then the proposed LPF model is derived by Taylor expansion. After only one initial regression learning, the proposed LPF model no longer needs retraining when updated. The refreshed parameter is simply updated online according to the real‐time measurement data, which improves the generalization ability. In conclusion, the proposed LPF model is accurate, generalizable, and greatly minimizes the data consumption and running time. Performance analysis verifies these superiorities.

Photoinhibition and photosynthetic regulation in fluctuating light under compound stresses of drought and heat

AbstractUnder the background of global climate change, crop leaves usually experience fluctuating light (FL) under compound stresses of drought and heat in the field. However, photoinhibition and photosynthetic regulation in FL under these compound stresses are little known. To elucidate this, we measured gas exchange, chlorophyll fluorescence, P700 redox state and electrochromic shift signals for tomato (Solanum lycopersicum) leaves exposed to FL under individual and compound stresses of moderate drought and heat stresses. After treatment with short‐term FL, photosystem I (PSI) activity decreased slightly in all treatments. By comparison, photosystem II (PSII) activity was reduced slightly under individual stress but largely decreased by 46% under compound stresses. Therefore, PSI is more tolerant than PSII when exposed to FL under compound stresses of drought and heat. Under compound stresses, PSII photoinhibition largely downregulated linear electron flow and photorespiration became a major electron sink downstream. Concomitantly, cyclic electron flow (CEF) was highly enhanced to help the building up of trans‐thylakoid proton gradient. This study highlights the importance of PSII activity and CEF in crop tolerance under future compound climate extremes such as drought and heat.

Thermal conductivity measurements for additively manufactured AlSi10Mg and Al6061-RAM2 Aluminum composites at cryogenic temperatures

Advances in 3D printing are disruptive opportunities for material selection and component design in cryogenics. However, thermophysical property measurements for these novel materials are generally unavailable at cryogenic temperatures. This experiment explores the variation in thermal conductivities due to print direction of two aluminium composites (AlSi10Mg and Al6061-RAM). The direct linear heat flow method was utilized to calculate thermal conductivities using a measured wattage input, temperature differential, and Fourier’s Law of Conduction. A multi-measurement linear regression was applied to determine thermal conductivities at fixed average temperatures over the range of 20-100K. The AlSi10Mg composite had a greater thermal conductivity than Al6061-T6 for both printing planes by approximately 230%. The XY-plane print direction resulted in a reduction in thermal conductivity compared with the Z-plane by approximately 30%. The AL6061-RAM composite had effective thermal conductivities smaller than the machined Al6061-T6 by approximately 70% for both print directions. The thermal conductivity in the Z-plane print direction was consistently greater than the thermal conductivity in the XY print direction. Validation studies were conducted utilizing Al6061-T6 and SS-304/304L. The calculated deviation for the validation samples depicted a 20% difference from the National Institute of Standards and Technologies (NIST) recommended reference values. The calculated uncertainty of the experimental system was 5-10%, increasing as temperature decreased. These preliminary measurements depict the need for further analysis on 3D printed composite materials and reverification of common materials due to improvements in current manufacturing methods since the classic experimental measurements were carried out for SS-304/304L and Al6061-T6.

Linear Power Flow Method for Radial Distribution Systems Including Voltage Control Devices

Linear Power Flow Method for Radial Distribution Systems Including Voltage Control Devices

Time-Dependent and Coating Modulation of Tomato Response upon Sulfur Nanoparticle Internalization and Assimilation: An Orthogonal Mechanistic Investigation.

Nanoenabled strategies have recently attracted attention as a sustainable platform for agricultural applications. Here, we present a mechanistic understanding of nanobiointeraction through an orthogonal investigation. Pristine (nS) and stearic acid surface-modified (cS) sulfur nanoparticles (NPs) as a multifunctional nanofertilizer were applied to tomato (Solanum lycopersicumL.) through soil. Both nS and cS increased root mass by 73% and 81% and increased shoot weight by 35% and 50%, respectively, compared to the untreated controls. Bulk sulfur (bS) and ionic sulfate (iS) had no such stimulatory effect. Notably, surface modification of S NPs had a positive impact, as cS yielded 38% and 51% greater shoot weight compared to nS at 100 and 200 mg/L, respectively. Moreover, nS and cS significantly improved leaf photosynthesis by promoting the linear electron flow, quantum yield of photosystem II, and relative chlorophyll content. The time-dependent gene expression related to two S bioassimilation and signaling pathways showed a specific role of NP surface physicochemical properties. Additionally, a time-dependent Global Test and machine learning strategy applied to understand the NP surface modification domain metabolomic profiling showed that cS increased the contents of IA, tryptophan, tomatidine, and scopoletin in plant leaves compared to the other treatments. These findings provide critical mechanistic insights into the use of nanoscale sulfur as a multifunctional soil amendment to enhance plant performance as part of nanoenabled agriculture.

Wave attenuation by three-dimensional circular floating sea ice: Regular and irregular waves

The evolution of ice conditions and wave patterns in polar water areas is complex, and studying the hydrodynamic response between sea ice and waves is crucial. In this study, the hydrodynamic response of sea ice in infinitely deep water is investigated by a sea ice scattering model based on linear potential flow and thin plate approximation theory. Building upon regular wave and sea ice scattering models, an irregular wave model was established and analyzed. This paper discusses the factors that influence sea ice resonance in a three-dimensional scattering model. It categorizes resonance phenomena into strong and weak based on mass and elasticity coefficients and provides a predictive function for identifying strong resonance points. Additionally, the study examines sea ice attenuation from an energy perspective. Research on sea ice in irregular waves indicates a negative correlation between the directional spreading parameter and wave attenuation. An increase in directional spreading parameter weakens the inhibitory effect on the high-frequency part of the waves. Increasing sea ice thickness enhances wave attenuation, exerting an inhibitory effect on waves in the high-frequency region.

On the extension of singular linear infinite-dimensional Hamiltonian flows

We study the phenomenon of phase trajectories of a Hamiltonian system going to infinity in a finite time, the phase space of which is a separable Hilbert space. It is shown that if the Hamiltonian is a densely defined quadratic form on the phase space, which is not majorized either from below or from above by the quadratic form of the Hilbert norm, then the phase trajectories allow going to infinity in a finite time. To describe the phase flow of such Hamiltonian systems, an extended phase space is introduced, which is a locally convex space to which the Hamiltonian function, trajectories of the Hamiltonian system, and the symplectic form defined on the original Hilbert space can be extended. Flowinvariant measures on extended space are also studied. The properties of the Koopman unitary representation of the extended phase flow in the Hilbert space of functions that are quadratically integrable with respect to an invariant measure are investigated.

An Experimental Study on the Seepage Characteristics of Rough Fractures in Coal under Stress Loading

Fracture and stress environments significantly affect the flow of coalbed methane. Under stress, fracture deformation and damage occur, which change the original fracture characteristics and lead to changes in gas flow characteristics. The change in gas pressure gradient makes the fluid flow obviously nonlinear. Using linear flow theory to describe the fracture flow leads to a large error in predicting coalbed methane productivity. In this study, seepage tests on fractured coal are carried out under different stresses and gas pressure gradients, the nonlinear flow and changes in related parameters are analyzed, and the applicability of the nonlinear flow equation is evaluated. The resulting seepage of the gas flow in the fracture under stress is obviously nonlinear, which gradually increases with increasing effective stress and gas pressure gradient. When the Forchheimer equation is used to characterize the nonlinear seepage in fractures, the coefficients increase with increasing effective stress. The permeability, nonlinear factor, and critical Reynolds number decrease with increasing effective stress. When the Izbash equation is used for this case, the linear coefficient ranges from 1015 to 1016, and the nonlinear coefficient ranges from 1.064 to 1.795. The coefficients are related to the effective stress through a power function. Both the Forchheimer and Izbash equations can characterize the flow in rough fractures in coal during stress loading. However, the Forchheimer equation better reveals the mechanism of flow transformation from linear to nonlinear in fractures.

A novel pressure transient analysis model for fracturing wells in fracture–cavity carbonate reservoirs

Large-scale karst caves are the principal storage spaces for hydrocarbon resources in fracture–cavity carbonate reservoirs. Drilling directly into these caves is considered the ideal mode of development, but many wells do not effectively penetrate karst caves. Therefore, acid fracturing is employed to generate artificial fractures that can connect with these caves. However, there are no appropriate well test methods for fracturing wells in fracture–cavity reservoirs. This study establishes a novel pressure transient analysis model for such wells. A new mathematical model is proposed that couples linear flow in acid fracturing cracks with radial flow in the oil drainage area. The Laplace transform and Stehfest numerical inversion provided analytical solutions for the bottomhole pressure. Typical log–log well testing curves were plotted to analyze oil flow, which occurs in ten stages. During the flow stage in fracturing cracks, the pressure and pressure derivative curves are parallel lines with a slope of 0.5. In the stage of karst cave storage, the pressure derivative curve is a straight line with a slope of 1. A comparison with previous models confirmed the validity of the proposed model. The influence of key parameters on the behavior of typical curves is analyzed. A field case study of the proposed model was carried out. Parameters related to fracturing cracks and karst caves, such as the crack length and cave radius, were successfully estimated. The proposed model has great potential for determining formation parameters of fracture–cavity reservoirs.

Long-term outcomes after formation of a low-flow STA-MCA bypass for treatment of symptomatic occlusion of the internal carotid artery

Aim. To evaluate short‑ and long‑term effectiveness of low‑flow bypass between superficial temporal artery and M4 segment of middle cerebral artery (low‑flow STA‑MCA bypass) in patients with symptomatic occlusion of the internal carotid artery (ICA).Materials and methods. Between 2016 and 2019 at the Department of Neurosurgery of the N. V. Sklifosovsky Research Institute of Emergency Medicine, 54 patients who underwent low‑flow STA‑MCA bypass formation at the side of symptomatic ICA occlusion between 2013 and 2015 were examined. Symptomatic ICA occlusion was more common in men than in women (7:1 ratio). Patient age varied between 48 and 73 years (mean age was 62 years).During low‑flow STA‑MCA bypass formation surgery for symptomatic ICA occlusion, intraoperative flowmetry was used in 52 (96 %) patients, in 2 (4 %) patients this diagnostic method was impossible to perform due to technical difficulties. The main examination methods in the long term after cerebral revascularization were evaluation of neurological status dynamics per the National Institute of Health Stroke Scale (NIHSS); modified Rankin scale; Rivermead mobility index; computed tomography angiography of the extra‑intracranial arteries; ultrasound (US) examination of the STA‑MCA bypass for eval uation of linear and volumetric blood flow velocities; single‑photon emission computed tomography. The type and size of trephination were evaluated, and operative time was taken into account.The patients were divided into 3 groups: group 1 included patients with follow‑up period of 1–2 years after cerebral revascularization, group 2 – 3–4 years, group 3 – 5–6 years. All results were compared to preoperative, early, and longterm measurements.Results. In the long‑term postoperative period between 1 and 6 years after cerebral revascularization, 54 patients were examined. Computed tomography angiography and US showed functioning STA‑MCA bypass in 53 (98 %) patients. According to single‑photon emission computed tomography of the brain, regional cerebral blood flow in the longterm postoperative period varied between 28 and 40 mL / 100 g / min, median regional cerebral blood flow in the long‑term postoperative period was 38 mL / 100 g / min. Intraoperative flowmetry was performed in 52 (96 %) patients, median was 15.5 mL / min. US showed that linear blood flow velocity in the STA‑MCA bypass varied between 20 and 95 cm / s, median was 49 cm / s. Volumetric blood flow varied between 30 and 85 mL / min with median of 75 mL / min.Resection trephination was performed in 36 (67 %) patients, mean size of trephination hole was 3 cm3. In the study, operative time was measured: mean value was 212 min; no significant correlation between operative time and trephination size was observed.Improved neurological status was observed in all study groups. Per the NIHSS, in group 1 (1–2 years) improvement was observed in 59 % of patients, in group 2 (3–4 years) in 48 %, in group 3 (5–6 years) in 47 %. Per the modified Rankin scale, in group 1 improvement was observed in 36.4 % of patients, in group 2 – in 48 %, in group 3 – in 42.9 %. Per the Rivermead mobility index, in group 1 improvement was observed in 63.3 % patients, in group 2 – in 56 %; in group 3 – in 57.1 %. The best outcomes were observed in group 1 (63.3 %).Conclusion. Instrumental diagnostic methods and evaluation of neurological status showed positive dynamics both in the postoperative period and in long‑term period between 1 and 6 years after low‑flow STA‑MCA bypass formation. In the long term, repeat abnormalities of cerebral blood flow of ischemic type and repeat transient ischemic attacks were not observed. Correct selection of patients in the preoperative period and comprehensive treatment including drug therapy in the postoperative and long‑term periods allow to prevent repeat ischemic cerebrovascular disease and therefore improve patients’ quality of life.

Role of Mass Transport in Electrochemical CO2 Reduction to Methanol Using Immobilized Cobalt Phthalocyanine.

Electrochemical CO2 reduction (CO2R) using heterogenized molecular catalysts usually yields 2-electron reduction products (CO, formate). Recently, it has been reported that certain preparations of immobilized cobalt phthalocyanine (CoPc) produce methanol (MeOH), a 6-electron reduction product. Here, we demonstrate the significant role of intermediate mass transport in CoPc selectivity to methanol. We first developed a simple, physically mixed, polymer (and polyfluoroalkyl, PFAS)-free preparation of CoPc on multiwalled carbon nanotubes (MWCNTs) which can be integrated onto Au electrodes using a poly(3,4-ethylenedioxythiophene) polystyrenesulfonate (PEDOT:PSS) adhesion layer. After optimization of catalyst preparation and loading, methanol Faradaic efficiencies and partial current densities of 36% (±3%) and 3.8 (±0.5) mA cm-2, respectively, are achieved in the CO2-saturated aqueous electrolyte. The electrolyte flow rate has a large effect. A linear flow velocity of 8.5 cm/min produces the highest MeOH selectivity, with higher flow rates increasing CO selectivity and lower flow rates increasing the hydrogen evolution reaction, suggesting that CO is an unbound intermediate. Using a continuum multiphysics model assuming CO is the intermediate, we show qualitative agreement with the optimal inlet flow rate. Polymer binders were not required to achieve a high Faradaic efficiency for methanol using CoPc and MWCNTs. We also investigated the role of formaldehyde as an intermediate and the role of strain, but definitive conclusions could not be established.

Instability in strongly stratified plane Couette flow, with application to supercritical fluids.

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft's criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831-864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g., miscible fluids) is finally discussed.

A three-dimensional numerical well-test model for pressure transient analysis in fractured horizontal wells with secondary fractures

During oil and gas reservoir development, multi-stage horizontal wells (MFHWs) and hydraulic fracturing techniques can effectively increase estimated ultimate recovery. However, there still lacks an understanding of the three-dimensional (3D) pressure transient behaviors of multi-stage fractured horizontal wells with secondary fractures. To narrow this gap, a three-dimensional numerical well-test model based on a discrete fracture model and unstructured tetrahedral grids is developed to study the pressure transient behaviors of MFHWs with secondary fractures. The pressure transient solutions of MFHWs with secondary fractures have been demonstrated by model verifications. The results show that the proposed model can accurately capture the complex transient flow around fractures, including early radial flow that is not easily captured by two-dimensional numerical well test models. The proposed model classifies the flow regimes of a MFHW as: wellbore storage and skin effects, early radial flow, bilinear flow, linear flow, elliptical flow, pseudo radial flow, and pseudo-boundary dominated flow. It is found that the fracture geometry has a relatively large effect on the shape of the pressure derivative curve in this work. The hydraulic fracture half-length has the greatest impact on the pressure transient behaviors of the MFHW, followed by fracture height and secondary fracture half-length, as found in this study. Additionally, fracture parameters are evaluated, and actual well testing data are interpreted, taking into account the fracture height. This work is meaningful to understand the three-dimensional pressure transient behaviors of MFHWs with secondary fractures.

A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies. However, the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis. This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions. The pressure-dependent length shrinkage coefficients, which quantify the length changes of the inner zone and propped fractures, are modified and incorporated into this multi-zone semi-analytical model. With simultaneous numerical iterations and numerical inversions in Laplace and real-time space, the transient solutions to pressure and rate behavior are determined in just a few seconds. The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods: fracture bilinear flow (FR1), dynamic PFs flow (FR2), inner-area linear flow (FR3), dynamic inner boundary flow (FR4), and outer-area dominated linear flow (FR5). The early hump during FR2 period and a positive upward shift during FR4 period are captured on the log-log pressure transient curves, reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary. The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly. The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves. If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected, the flow rate will be overestimated in the later production period.

Hydrodynamic performance of vertical cylindrical wave energy absorbers in front of a vertical wall

This paper studies the hydrodynamic performance of vertical cylindrical absorbers in front of a vertical wall. All the absorbers are independent of each other and restricted to only the heave motion. Based on a linear potential flow theory, an analytical solution is developed for the problems of wave diffraction and radiation by absorbers. In the solving procedure, the hydrodynamic problem is first transformed into an equivalent problem in an open water domain using the image principle. The number of absorbers in the equivalent problem is twice that in the real problem, and the plane layout is symmetric about the original vertical wall. The velocity potential of the fluid domain is obtained using the method of variable separation, and the unknown expansion coefficients in the velocity potential are determined by the matched boundary conditions. The heave excitation force, added mass, radiation damping, motion response, and energy capture width of the absorbers are calculated. Case studies are presented to show the effects of the wall reflection and hydrodynamic interaction on the energy extraction performance of the wave energy converter (WEC) system. Subsequently, the WEC performance under the action of irregular waves is analyzed by considering an incident wave spectrum, and the mean annual absorbed power of the device is estimated by considering the wave data statistics at the actual sites. The results indicate that when the wave motion resonates with the absorber motion, the energy extraction performance of the absorbers is significantly improved. The performance of the absorbers can be effectively improved when the structures are close to the antinodes of a standing wave field. By designing a reasonable plane layout, the hydrodynamic interaction can play a constructive role in the performance of the WEC system.

Design and optimization of liquid-cooled plate structure for power battery of the pure electric excavator

With the increasing pressure of energy transformation and environmental protection, the trend of electrification of construction machinery is becoming more and more obvious. In this paper, based on a small pure electric excavator which is still in the stages of research and development, a liquid-cooled heat dissipation structure (liquid-cooled plate) is designed according to the power battery pack scheme. The overall shape of the liquid-cooled plate is designed as a symmetrical serpentine flow channel. Geometrically, the symmetrical serpentine flow channel is a combination of a straight flow channel and a runway-shaped flow channel. Then the conjugate heat transfer simulation model was established by using the CFD software Ansys Fluent. The results show that the initial scheme can not guarantee the temperature homogeneity of the battery pack. Therefore, the liquid-cooled heat dissipation scheme was optimized and compared. Firstly, a liquid-cooled plate was added on the original basis, and multiple sets of simulations were carried out with the length of the linear flow channel as a variable. The results show that appropriately increasing the length of the straight flow channel at the entrance of the liquid-cooled plate has a marked effect on improving the heat dissipation performance.

A design of a nature-like fishway to solve the fractured river connectivity caused by small hydropower based on hydrodynamics and fish behaviors.

Achieving a harmonious alignment between the biological characteristics of fish and hydrodynamics patterns is crucial for ensuring the efficacy of fish passage facilities. In this study, based on the hydrodynamic characteristics of the river and the biological characteristics of fish, we evaluated the internal flow field in the nature-like fishway of Congen II hydropower station located along the Chabao river and explored methods to improve the operation efficiency. Based on comprehensive considerations of the flow field, turbulent kinetic energy, and the migration pathways of fish, it is found that the implementation of a continuous oblique bottom slope represents a more cost-effective and operationally convenient solution. The influence of different permutation of bulkheads in the nature-like fishway on operational efficiency was further examined. Our investigation revealed that the nature-like fishway with the continuous slope of 2% and the arrangement of three bulkheads in each row (model 3) exhibited a relatively simple velocity distribution and linear flow line, which poses challenges for fish in locating resting areas. In addition, the distribution of low turbulence kinetic energy area in the mainstream made it less favorable for fish to transition from the mainstream to the rest area within the fishway. The nature-like fishway with the continuous slope of 2% and the arrangement of two or three bulkheads in staggered rows (model 4) demonstrated better performance. Several potential fish migration routes for both model 3 and model 4 were proposed based on the numerical simulation results. In model 3, fish exhibited a continuous sprint through the concentrated high-speed area, which was less favorable for fish to rest and forage. In contrast, model 4 exhibited a diversified flow velocity distribution, enabling fish to make timely changes in their direction during migration. This feather proved to be advantageous in enhancing fish migration within the passage. The design of nature-like fishway in this study provides an important reference and technical support for the construction and optimization of the nature-like fishway for low dams, and is of great significance for restoring river connectivity destroyed by small hydropower construction and improving fish migration.

Representation formulae for linear hyperbolic curvature flows

In [19], Smoczyk showed that parabolic expansion of convex curves and hypersurfaces by the reciprocal of the harmonic mean curvature gives rise to a linear second order equation for the evolution of the support function, with corresponding representation formulae for solutions. In this article we obtain representation formula for the corresponding linear hyperbolic evolution equation for the support function of locally convex curves of general nonzero rotation number, finding some natural similarities and differences in behaviour of solutions as compared with the parabolic case. As applications, we consider linear hyperbolic flows that preserve length or generalised enclosed area of the evolving curve, flow of curves with Neumann boundary conditions inside cones and hyperbolic approaches to the Yau problem of flowing one curve to another. We also consider radial graphs evolving by similar linear equations and linear higher order hyperbolic equations. Our results may be compared with the corresponding parabolic cases consider by the first author, Schrader and Wheeler, in [17].