Finite Pressure Research Articles

Existence of the zero-temperature limit of equilibrium states on topologically transitive countable Markov shifts

AbstractConsider a topologically transitive countable Markov shift $\Sigma $ and a summable locally constant potential $\phi $ with finite Gurevich pressure and $\mathrm {Var}_1(\phi ) < \infty $ . We prove the existence of the limit $\lim _{t \to \infty } \mu _t$ in the weak $^\star $ topology, where $\mu _t$ is the unique equilibrium state associated to the potential $t\phi $ . In addition, we present examples where the limit at zero temperature exists for potentials satisfying more general conditions.

The finite deformation approximate solution and pressure–impulse​ diagram of an elastic–brittle rectangular glass plate under pressure loading

Glass windows and curtain walls are increasingly used in modern buildings. To judge whether a glass panel fails under a certain blast, the pressure–impulse (P–I) diagram is necessary. In contrast to the commonly adopted P–I diagrams given by the single degree of freedom theory or the high-cost finite element (FE) simulations, a P–I diagram is given in this study by employing a proposed approximate analytical solution. The theoretical solution of the finite deformation rectangular plate under pressure loading is based on the traditional von Kármán equations and the uniform stress assumption. Through comparisons with the corresponding FE simulations, experimental data, and internationally acknowledged standards, the solution is confirmed to be both accurate and efficient. Furthermore, the P–I diagram given is also confirmed to be both reliable and efficient when compared with the experimental data.

Numerical analysis of the spatial structure of Alfvén waves in a finite pressure plasma in a dipole magnetosphere

We have carried out a numerical analysis of the spatial structure of Alfvén waves in a finite pressure inhomogeneous plasma in a dipole model of the magnetosphere. We have considered three magnetosphere models differing in maximum plasma pressure and pressure gradient. The problem of wave eigenfrequencies was addressed. We have established that the poloidal frequency can be either greater or less than the toroidal frequency, depending on plasma pressure and its gradient. The problem of radial wave vector component eigenvalues was considered. We have found points of Alfvén wave reflection in various magnetosphere models. The wave propagation region in the cold plasma model is shown to be significantly narrower than that in models with finite plasma pressure. We have investigated the structure of the main Alfvén wave harmonic when its polarization changes in three magnetosphere models. A numerical study into the effect of plasma pressure on the structure of behavior of all Alfvén wave electric and magnetic field components has been carried out. We have established that for certain parameters of the magnetosphere model the magnetic field can have three nodes, whereas in the cold plasma model there is only one. Moreover, the longitudinal magnetic field component changes sign twice along the magnetic field line.

Численный анализ пространственной структуры альфвеновских волн в плазме конечного давления в дипольной магнитосфере

We have carried out a numerical analysis of the spatial structure of Alfvén waves in a finite pressure inhomogeneous plasma in a dipole model of the magnetosphere. We have considered three magnetosphere models differing in maximum plasma pressure and pressure gradient. The problem of wave eigenfrequencies was addressed. We have established that the poloidal frequency can be either greater or less than the toroidal frequency, depending on plasma pressure and its gradient. The problem of radial wave vector component eigenvalues was considered. We have found points of Alfvén wave reflection in various magnetosphere models. The wave propagation region in the cold plasma model is shown to be significantly narrower than that in models with finite plasma pressure. We have investigated the structure of the main Alfvén wave harmonic when its polarization changes in three magnetosphere models. A numerical study into the effect of plasma pressure on the structure of behavior of all Alfvén wave electric and magnetic field components has been carried out. We have established that for certain parameters of the magnetosphere model the magnetic field can have three nodes, whereas in the cold plasma model there is only one. Moreover, the longitudinal magnetic field component changes sign twice along the magnetic field line.

Maximization of heat transfer density from radially finned tubes in cross‐flow using the constructal design method

AbstractThe maximization of volumetric heat transfer density from radially finned tubes in cross‐flow is investigated in this study based on the constructal design method. A row of radially finned tubes is placed in cross‐air flow. The tubes and the radial fins are heated at uniform temperatures and cooled by the air cross‐flow. The cross‐air flow is generated by a finite pressure difference. Two dimensionless pressure differences (Bejan number) are considered (Be = 103 and Be = 105). The objective function, the degrees of freedom, and the constraints in the constructal design method should be identified. The objective function is the maximization of the heat transfer density from the finned tubes. The degrees of freedom are; the fin tip‐to‐fin tip spacing, the number of fins, the tube diameter, the fin thickness, and the angle between the fins. The constraints are the length and height of the space occupied by the finned tubes. The pressure‐driven flow and energy equations (steady, two‐dimensional, and incompressible) are solved by means of the finite volume method. The ranges of the dimensionless fin tip‐to‐fin tip spacing are (0.2 ≤ S ≤ 1 for Be = 103 and 0.05≤ S ≤ 0.3 for Be = 105). The number of fins is changed as (N = 2, 4, 6, 8, 10, and 12). The dimensionless tube diameter is changed as (D = 0.25, 0.5, and 0.75). The dimensionless fin thickness is changed as (T = 0.001, 0.01, and 0.05). The results showed that for both (Be = 103) and (Be = 105), the highest value of the maximum volumetric heat transfer density is for (N = 2) and decreases as the number of fins increases. In addition, the minimum values of the maximum volumetric heat transfer density occur when the vertical fins exist at (N = 4, 8, and 12).

Estimating wind velocity and direction using sparse sensors on a cylinder

Using finite pressure measurements on a cylinder, we are able to estimate both the oncoming wind speed and direction of uniform flow over a cylinder at Reynolds numbers 20 000<Re<120 000. While reduced-order methods, such as proper orthogonal decomposition with QR factorization, require at least nine sensors to estimate the oncoming wind speed and direction with <10% error, other methods, such as probabilistic approaches or curve-fitting, can achieve similar results with as few as five sensors. A utility function, based on the Kullback–Leibler divergence, is used to determine the locally optimal location of the sensors to accurately estimate inlet conditions. It was found that sensor arrangement also plays a significant role, with unevenly distributed sensors being preferable than evenly distributed sensors. These techniques, when paired with existing flow field estimation approaches, allow the user to predict the surrounding flow field from any oncoming direction.

Design and optimization of cylindrical hull with non-uniform arch ribs for underwater gliders based on approximate model and experiments

The underwater glider is one of the most promising autonomous underwater vehicles for long-term ocean observations, whose battery capacity and energy consumption are directly affected by compressibility and buoyancy factor of its pressure hull. Thus, to further increase compressibility and decrease buoyancy factor of underwater vehicles, this study proposes a cylindrical hull with non-uniform arch ribs by analyzing design and test results of the existing hulls used in the Petrel-L glider, China. Considering complexity of the proposed cylindrical hull, the approximate model of mass and other output responses of hull is established based on a parametric model by response surface method, which is used to optimize design variables and thus obtain an optimal cylindrical hull. Additionally, the performance of the optimal hull is verified by finite element method and pressure tests. Compared with a conventional cylindrical hull, the deformation of optimal hull is increased by 38.79%, which can indirectly reduce the energy consumption of the buoyancy drive unit and improve endurance of the Petrel-L glider. Meanwhile, the mass of the optimal hull is decreased by 21.57%, which allows more battery or sensor load under the same pressure. Furthermore, the proposed hull can apply to other underwater vehicles.

Возмущения второго порядка в альфвеновских волнах в плазме с давлением

It is shown first that in finite pressure plasma, just as in cold plasma, Alfvén waves created by an initial perturbation generate plasma flows and decreases in the magnetic field, which propagate along with these waves. Second, at the stage of their interaction, Alfvén waves generate slow magnetosonic (SMS) waves propagating along the magnetic field. These results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves both in the magnetosphere regions with cold plasma and in the magnetosphere regions with finite pressure plasma. They also provide potential possibility for determining the position of a source of Alfvén disturbance from observations of Alfvén waves and their induced SMS waves.

Second-order perturbations in Alfvén waves in finite pressure plasma

It is shown first that in finite pressure plasma, just as in cold plasma, Alfvén waves created by an initial perturbation generate plasma flows and decreases in the magnetic field, which propagate along with these waves. Second, at the stage of their interaction, Alfvén waves generate slow magnetosonic (SMS) waves propagating along the magnetic field. These results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves both in the magnetosphere regions with cold plasma and in the magnetosphere regions with finite pressure plasma. They also provide potential possibility for determining the position of a source of Alfvén disturbance from observations of Alfvén waves and their induced SMS waves.

Piezoelectric Hydrogel for Prophylaxis and Early Treatment of Pressure Injuries/Pressure Ulcers.

Pressure injuries/pressure ulcers (PIs/PUs) are a critical global healthcare issue and represent a considerable burden on healthcare resources. Prevention of PIs/PUs is the least costly approach and minimizes the patient suffering compared with treatment. Besides, sustained tissue load alleviation and microenvironment management are the most crucial properties for dressings in PI/PU prevention. Hydrogel dressings have attracted a lot of attention to prevent PIs/PUs because of their unique mechanical properties and ability to manage the microenvironment of skin. However, auxiliary prophylaxis and early treatment of PIs/PUs remain a challenge and an acute clinical demand. Here, we report on an electroactive hydrogel with large stretchability (∼380%) and skinlike ductility, and Young's modulus (0.48 ± 0.03 MPa) matches that of human skin (0.5-1.95 MPa). The hydrogel displayed piezoelectric properties and mechanical-electric response stability and sensitivity. Our results indicated that the hydrogel was able to promote in vitro angiogenesis under piezoelectric stimulation and exhibited biocompatibility, which has the potential for forming fine vessels at the damaged sites of PIs/PUs. Furthermore, finite element analysis and pressure dispersion experiments demonstrated that the hydrogel was suitable for preventing PIs/PUs by redistributing force, reducing tissue distortion, and maintaining the microenvironment for skin. This work offers a new strategy for designing and evaluating the dressing for prophylaxis and the early treatment of PIs/PUs.

Angiodynamic and optical coupling analysis of skin tissue model under finite pressure

The pulse amplitude of fingertip volume could be improved by selecting the vascular dense area and applying appropriate pressure above it. In view of this phenomenon, this paper used Comsol Multiphysics 5.6 (Comsol, Sweden), the finite element analysis software of multi-physical field coupling simulation, to establish the vascular tissue model of a single small artery in fingertips for simulation. Three dimensional Navier-Stokes equations were solved by finite element method, the velocity field and pressure distribution of blood were calculated, and the deformation of blood vessels and surrounding tissues was analyzed. Based on Lambert Beer's Law, the influence of the longitudinal compression displacement of the lateral light surface region and the tissue model on the light intensity signal is investigated. The results show that the light intensity signal amplitude could be increased and its peak value could be reduced by selecting the area with dense blood vessels. Applying deep pressure to the tissue increased the amplitude and peak of the signal. It is expected that the simulation results combined with the previous experimental experience could provide a feasible scheme for improving the quality of finger volume pulse signal.

A Prototype Design and Sea Trials of an 11,000 m Autonomous and Remotely-Operated Vehicle Dream Chaser

To better study the biology and ecology of hadal trenches for marine scientists, the Hadal Science and Technology Research Center (HAST) of Shanghai Ocean University proposed to construct a movable laboratory that includes a mothership, several full-ocean-depth (FOD) submersibles, and FOD landers to obtain samples in the hadal trenches. Among these vehicles, the project of an FOD autonomous and remotely-operated vehicle (ARV) named “Dream Chaser” was started in July 2018. The ARV could work in both remotely-operated and autonomous-operated modes, and serves large-range underwater observation, on-site sampling, surveying, mapping, etc. This paper proposed a novel three-body design of the FOD ARV. A detailed illustration of the whole system design method is provided. Numerical simulations and experimental tests for various sub-systems and disciplines have been conducted, such as resistance analysis using the computational fluid mechanics method and structural strength analysis for FOD hydrostatic pressure using the finite element method and pressure chamber tests. In addition, components tests and the entire system tests have been performed on land, underwater, and in the pressure chamber in the laboratory of HAST, and the results are discussed. Extensive experiments of two critical components, i.e., the thrusters and ballast-abandoning system, have been conducted and further analyzed in this paper. Finally, the procedures and results of lake trials, South China Sea trials and the first phase of Mariana Trench sea trials of the ARV in 2020 are also introduced. This paper provides a design method for the novel three-body FOD ARV. More importantly, the lessons learned from the FOD pressure test, lake tests, and sea trials, no matter the success or failure, will guide future endeavors and the application of ARV Dream Chaser and underwater vehicles of this kind.

New Dimensionless Number for the Transition from Viscous to Turbulent Flow

Within the framework of Classical Continuum Thermomechanics, we consider an unsteady isothermal flow of a simple isotropic linear viscous fluid in the liquid state to investigate the transient flow conditions. Despite the attention paid to this problem by several research works, it seems that the understanding of turbulence in these flow conditions is controversial. We propose a dimensionless procedure that highlights some aspects related to the transition from viscous to turbulent flow which occurs when a finite amplitude pressure wave travels through the fluid. This kind of transition is demonstrated to be described by a (first) dimensionless number, which involves the bulk viscosity. Furthermore, in the turbulent flow regime, we show the role played by a (second) dimensionless number, which involves the turbulent bulk viscosity, in entropy production. Within the frame of the 1D model, we test the performance of the dimensionless procedure using experimental data on the pressure waves propagation in a long pipe (water hammer phenomenon). The obtained numerical results show good agreement with the experimental data. The results’ inspection confirms the predominant role of the turbulent bulk viscosity on energy dissipation processes.

Toroidal modeling of energetic passing particle drift kinetic effects on tearing mode stability

Drift kinetic effects of the neutral beam injection induced passing energetic particles (EPs) on the linear stability of the n = 1 tearing mode (TM) (with the dominant poloidal harmonic of m = 2) are numerically investigated utilizing the MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503), in a tokamak plasma with finite equilibrium pressure and anisotropic thermal transport. In the low plasma pressure regime, it is found that co- (counter-) passing EPs stabilize (destabilize) the TM, agreeing with previous studies. However, as the plasma pressure increases beyond a critical value, it is found that co-passing EPs also destabilize the mode. An in-depth analysis reveals that the net effect of co-passing EPs is a result of competition between the stabilizing contribution from the non-adiabatic drift kinetic terms and the destabilizing contribution associated with adiabatic terms, with the latter becoming more dominant at higher equilibrium pressure. Non-perturbative magnetohydrodynamic-kinetic hybrid modeling also finds that co- and counter-passing EPs modify the TM eigenfunction differently, with the counter-passing EPs enhancing the sideband harmonics. Furthermore, effects of the plasma resistivity and toroidal rotation, as well as that of the equilibrium distribution of EPs in the particle pitch angle space, are also investigated, showing asymmetric results on the TM stability between the co- and counter-passing EPs. The first order finite orbit width correction is found to be stabilizing with co-passing EPs and destabilizing with counter-passing particles. Finally, drift resonances between passing EPs and the TM induce finite frequency to the mode and generate finite net torques inside the plasma, due to the neoclassical toroidal viscosity and the Reynolds stress associated with 3D perturbations.

Poroelastic modeling of pore pressure development in granular pavement layers

ABSTRACT Moisture excess in granular pavement layers can decrease pavement performance leading to moisture-related distresses. The combination of trapped water and heavy traffic loads may substantially increase pore pressure and lead to shear failure if layer hydraulic conductivity is insufficient. Currently, most pavement analysis models are unable to predict pore pressure development, so the design and evaluation methods ignore this dynamic effect which may significantly underestimate the moisture damaging effect on pavements. This paper proposes the use of Biot’s poroelasticity theory for modelling fully saturated unbound materials. The proposed methodology – Poroelastodynamic Finite Integration Technique (PEFIT) – was used to analyze axisymmetric multilayered pavement structures consisting of elastic and poroelastic layers. The model was verified and validated using a well-known commercial finite element solver and field pore pressure data, respectively. A sensitivity analysis was conducted by varying critical pavement design parameters. The PEFIT analysis of a three-layer pavement system with a poroelastic base layer has shown that a decrease in base hydraulic conductivity significantly increases the maximum pore pressure, especially for high-speed loads. Results also indicate substantial pore pressure and water movement in the base layer, which may induce a potential shear failure mechanism for unbound materials.

Detectable universes inside regular black holes

While spacetime in the vicinity outside astrophysical black holes is believed to be well understood, the event horizon and the interior remain elusive. Here, we discover a degenerate infinite spectrum of novel general relativity solutions with the same mass-energy and entropy that describe a dark energy universe inside an astrophysical black hole. This regular cosmological black hole is stabilized by a finite tangential pressure applied on the dual cosmological-black hole event horizon, localized up to a quantum indeterminacy. We recover the Bekenstein–Hawking entropy formula from the classical fluid entropy, calculated at a Tolman temperature equal to the cosmological horizon temperature. We further calculate its gravitational quasi-normal modes. We find that cosmological black holes are detectable by gravitational-wave experiments operating within the mu mathrm{Hz}–mathrm{Hz} range, like LISA space-interferometer.

CARNOT: a Fragment-Based Direct Molecular Dynamics and Virtual-Reality Simulation Package for Reactive Systems.

Traditionally, the study of reaction mechanisms of complex reaction systems such as combustion has been performed on an individual basis by optimizations of transition structure and minimum energy path or by reaction dynamics trajectory calculations for one elementary reaction at a time. It is effective, but time-consuming, whereas important and unexpected processes could have been missed. In this article, we present a direct molecular dynamics (DMD) approach and a virtual-reality simulation program, CARNOT, in which plausible chemical reactions are simulated simultaneously at finite temperature and pressure conditions. A key concept of the present ab initio molecular dynamics method is to partition a large, chemically reactive system into molecular fragments that can be adjusted on the fly of a DMD simulation. The theory represents an extension of the explicit polarization method to reactive events, called ReX-Pol. We propose a highest-and-lowest adapted-spin approximation to define the local spins of individual fragments, rather than treating the entire system by a delocalized wave function. Consequently, the present ab initio DMD can be applied to reactive systems consisting of an arbitrarily varying number of closed and open-shell fragments such as free radicals, zwitterions, and separate ions found in combustion and other reactions. A graph-data structure algorithm was incorporated in CARNOT for the analysis of reaction networks, suitable for reaction mechanism reduction. Employing the PW91 density functional theory and the 6-31+G(d) basis set, the capabilities of the CARNOT program were illustrated by a combustion reaction, consisting of 28 650 atoms, and by reaction network analysis that revealed a range of mechanistic and dynamical events. The method may be useful for applications to other types of complex reactions.

Superconductor–insulator transitions in three-dimensional indium-oxide at high pressures

Experiments investigating magnetic-field-tuned superconductor–insulator transition (HSIT) mostly focus on two-dimensional material systems where the transition and its proximate ground-state phases, often exhibit features that are seemingly at odds with the expected behavior. Here we present a complementary study of a three-dimensional pressure-packed amorphous indium-oxide (InOx) powder where granularity controls the HSIT. Above a low threshold pressure of ∼0.2 GPa, vestiges of superconductivity are detected, although neither a true superconducting transition nor insulating behavior are observed. Instead, a saturation at very high resistivity at low pressure is followed by saturation at very low resistivity at higher pressure. We identify both as different manifestations of anomalous metallic phases dominated by superconducting fluctuations. By analogy with previous identification of the low resistance saturation as a ‘failed superconductor’, our data suggests that the very high resistance saturation is a manifestation of a ‘failed insulator’. Above a threshold pressure of ∼6 GPa, the sample becomes fully packed, and superconductivity is robust, with T C tunable with pressure. A quantum critical point at P C ∼ 25 GPa marks the complete suppression of superconductivity. For a finite pressure below P C, a magnetic field is shown to induce a HSIT from a true zero-resistance superconducting state to a weakly insulating behavior. Determining the critical field, H C, we show that similar to the 2D behavior, the insulating-like state maintains a superconducting character, which is quenched at higher field, above which the magnetoresistance decreases to its fermionic normal state value.

Buckling of a Composite Cylindrical Shell with Cantilever-like Boundary Conditions under Hydrostatic Pressure

In this study, an analytical solution for the buckling of a composite cylindrical shell subjected to hydrostatic pressure is proposed. The boundary conditions of the composite cylindrical shell are cantilever-like, with one end fixed and the other end connected to a rigid disk. The differential equations are solved using the Galerkin method. The axial displacement of the shell is approximated by the first mode shape of the transverse vibration of the clamped sliding beam. The circumferential displacement and deflection are approximated by the first derivation of the beam function. Based on this solution, an analytical formula enabling prediction of the critical buckling pressure and buckling mode of composite orthotropic cylindrical shells is derived. A finite element analysis and external hydrostatic pressure test are conducted to verify the proposed approach. The efficiency and accuracy of the analytical solution in predicting the critical buckling pressure and buckling mode are demonstrated.

Soil Pressure and Deformation Analysis of Small Size Deep Foundation Pit

In this paper, the influence of space effect on soil pressure and deformation of deep foundation pit was considered, and the finite soil pressure calculation model was established. The soil pressure of deep foundation pit was calculated by assuming the slip surface and using the finite soil limit equilibrium theory. Then, PLAXIS 3D finite element software was used to establish finite element models of different plane sizes and depths. The distribution regulation of side wall soil pressure and deformation of deep foundation pit was calculated. Finally, the results of finite soil pressure calculation was compared with finite element method. The results shown that: The soil pressure of small deep foundation pit was affected by space effect, and the soil pressure and deformation decrease significantly along the foundation pit depth. Shear fracture Angle was related to the ratio of width to depth of foundation pit, and it was no longer a constant value of 45°+φ/2. Therefore, the spatial effect should be considered in the calculation of soil pressure of small deep foundation pit. The research results can provide some guidance for the design and calculation of similar small size deep foundation pit.