Static Initial Conditions Research Articles

Vertical escape tactics and movement potential of orthoconic cephalopods.

Measuring locomotion tactics available to ancient sea animals can link functional morphology with evolution and ecology over geologic timescales. Externally-shelled cephalopods are particularly important for their central roles in marine trophic exchanges, but most fossil taxa lack sufficient modern analogues for comparison. In particular, phylogenetically diverse cephalopods produced orthoconic conchs (straight shells) repeatedly through time. Persistent re-evolution of this morphotype suggests that it possesses adaptive value. Practical lateral propulsion is ruled out as an adaptive driver among orthoconic cephalopods due to the stable, vertical orientations of taxa lacking sufficient counterweights. However, this constraint grants the possibility of rapid (or at least efficient) vertical propulsion. We experiment with this form of movement using 3D-printed models of Baculites compressus, weighted to mimic hydrostatic properties inferred by virtual models. Furthermore, model buoyancy was manipulated to impart simulated thrust within four independent scenarios (Nautilus-like cruising thrust; a similar thrust scaled by the mantle cavity of Sepia; sustained peak Nautilus-like thrust; and passive, slightly negative buoyancy). Each model was monitored underwater with two submerged cameras as they rose/fell over ~2 m, and their kinematics were computed with 3D motion tracking. Our results demonstrate that orthocones require very low input thrust for high output in movement and velocity. With Nautilus-like peak thrust, the model reaches velocities of 1.2 m/s (2.1 body lengths per second) within one second starting from a static initial condition. While cephalopods with orthoconic conchs likely assumed a variety of life habits, these experiments illuminate some first-order constraints. Low hydrodynamic drag inferred by vertical displacement suggests that vertical migration would incur very low metabolic cost. While these cephalopods likely assumed low energy lifestyles day-to-day, they may have had a fighting chance to escape from larger, faster predators by performing quick, upward dodges. The current experiments suggest that orthocones sacrifice horizontal mobility and maneuverability in exchange for highly streamlined, vertically-stable, upwardly-motile conchs.

Inhibition of premature transient boiling crisis induced by heat-load step pulses in a helium natural circulation loop by dynamic initial condition

Boiling helium natural circulation loops constitute a cooling option for large superconducting magnets. Their steady state thermalhydraulic behavior has already been studied quite thoroughly. However, the transient response of these systems has started being studied only recently. Although transient boiling experiments with other fluids or heating configurations exist, their findings are difficult to extrapolate to the case of natural circulation loops. In this work, we present the continuation of an experimental study on helium natural circulation loops. In this case, the system is excited by a stepwise power increase from a dynamic initial condition (a stable initial heat flux is applied). Boiling crisis onset during the transient was identified from the measurement of wall temperature on the heated section. The increase of the initial heat flux and the consequent initial flow increase have been found to have a partial or complete inhibiting effect on transient boiling crisis onset in the premature boiling crisis regime with respect to the static initial condition case. Behavior charts could be drawn on the initial-final heat flux plane. A general empirical criterion based on the evolution of vapor fraction along the section is provided for the prediction of boiling crisis onset by this mechanism.

Study on control mode of operation parameter in hydropower air chamber

This paper makes a deep analysis on PL control mode and static water level control mode, which could control operation parameters more conveniently and ensure safety and stability of hydropower water conveyance system. Considering the physical circumstance of monitoring parameters of the air chamber, the mathematic model of air chamber is built. On the basis of two basic criteria which are the maximum pressure at the end of spiral case and the down surge of the air chamber in hydraulic transient process, one hydropower station with air chamber is taken as an example. Determined by the effects of the upper reservoir water level on monitoring parameters, the allowable ranges of PL and air height could be consulted to control actuating and impeding the air compressor and the exhaust valve in an appropriate way. It is put forward that the maximum (minimum) product of the pressure and air height under dynamic initial condition, the maximum (minimum) air height under dynamic initial condition and static initial condition are determined by the criteria of down surge in the air chamber with large volume air (the criteria of the maximum pressure at the end of the spiral case with small volume air).

Design and Characterization of an Exoskeleton for Perturbing the Knee During Gait.

An improved understanding of mechanical impedance modulation in human joints would provide insights about the neuromechanics underlying functional movements. Experimental estimation of impedance requires specialized tools with highly reproducible perturbation dynamics and reliable measurement capabilities. This paper presents the design and mechanical characterization of the ETH Knee Perturbator: an actuated exoskeleton for perturbing the knee during gait. A novel wearable perturbation device was developed based on specific experimental objectives. Bench-top tests validated the device's torque limiting capability and characterized the time delays of the on-board clutch. Further tests demonstrated the device's ability to perform system identification on passive loads with static initial conditions. Finally, the ability of the device to consistently perturb human gait was evaluated through a pilot study on three unimpaired subjects. The ETH Knee Perturbator is capable of identifying mass-spring systems within 15% accuracy, accounting for over 95% of the variance in the observed torque in 10 out of 16 cases. Five-degree extension and flexion perturbations were executed on human subjects with an onset timing precision of 2.52% of swing phase duration and a rise time of 36.5ms. The ETH Knee Perturbator can deliver safe, precisely timed, and controlled perturbations, which is a prerequisite for the estimation of knee joint impedance during gait. Tools such as this can enhance models of neuromuscular control, which may improve rehabilitative outcomes following impairments affecting gait and advance the design and control of assistive devices.

Dissipative axial inflation

We analyze in detail the background cosmological evolution of a scalar field coupled to a massless abelian gauge field through an axial term ϕ/fγ F ̃F, such as in the case of an axion. Gauge fields in this case are known to experience tachyonic growth and therefore can backreact on the background as an effective dissipation into radiation energy density ρR, which can lead to inflation without the need of a flat potential. We analyze the system, for momenta k smaller than the cutoff fγ, including the backreaction numerically. We consider the evolution from a given static initial condition and explicitly show that, if fγ is smaller than the field excursion ϕ0 by about a factor of at least \U0001d4aa (20), there is a friction effect which turns on before the field can fall down and which can then lead to a very long stage of inflation with a generic potential. In addition we find superimposed oscillations, which would get imprinted on any kind of perturbations, scalars and tensors. Such oscillations have a period of 4–5 efolds and an amplitude which is typically less than a few percent and decreases linearly with fγ. We also stress that the curvature perturbation on uniform density slices should be sensitive to slow-roll parameters related to ρR rather than ϕ̇2/2 and we discuss the existence of friction terms acting on the perturbations, although we postpone a calculation of the power spectrum and of non-gaussianity to future work and we simply define and compute suitable slow roll parameters. Finally we stress that this scenario may be realized in the axion case, if the coupling 1/fγ to U(1) (photons) is much larger than the coupling 1/fG to non-abelian gauge fields (gluons), since the latter sets the range of the potential and therefore the maximal allowed ϕ0∼ fG.

Transient boiling crisis induced by heat-load step pulses in a helium vertically heated natural circulation loop with static initial condition

Boiling helium natural circulation loops are used as cooling system of some large superconducting magnets. Their thermalhydraulic behavior has already been studied quite thoroughly in steady state operation. However, the transient response of these systems remains up to date poorly studied, and transient boiling experiments in other fluids or heating configurations are difficult to extrapolate. In this work, an experimental study of helium natural circulation loops is conducted in which the system is excited by a step-pulse power wave function from a static initial condition (no power applied). The measurements of wall temperature on the heated section allowed the detection of boiling crisis onset during the transient. Different boiling crisis onset mechanisms could be determined from the dependence of the nucleate boiling lifetime on applied heat flux. The simultaneous analysis of thermal aspects and mass flow rate evolution allowed determining a semi-empirical local criterion based on the evolution of vapor fraction along the section for the prediction of transient boiling crisis.

Fuzzy cognitive maps and cellular automata: An evolutionary approach for social systems modelling

One of the first decisions to be made when modelling a phenomenon is that of scale: at which level is the phenomenon most appropriately modelled? For some phenomena the answer may seem too obvious to warrant even asking the question, but other phenomena cover the gamut, from high to low levels of abstraction. This paper explores how two modelling approaches that are ‘at home’ at opposite ends of the abstraction spectrum can be combined to yield an evolutionary modelling approach that is especially apt for phenomena that cover a wide range in this spectrum.We employ fuzzy cognitive maps (FCMs) to model the interplay between high-level concepts, and cellular automata (CA) to model the low-level interactions between individual actors. The combination of these models carries both beyond their respective limitations: the FCM concept is extended beyond the derivation of equilibrium outcomes from static initial conditions, to time-evolving systems where conditions may vary; CA are extended beyond the emergence of patterns from local interactions, to systems where global patterns have local repercussions.The applicability of the methodology is demonstrated by modelling the spread of human immunodeficiency virus (HIV) in an environment in which injection drug users share paraphernalia.

Perturbation Theory for Hamilton's Principal Function

OLUTIONStotwo-pointboundaryvalueproblems(2BVPs)are of significant importance in the field of astrodynamics and have been subject to extensive research over the years. However, the lack of procedures that automatically converge to the desired solution remains as a fundamental difficulty in solving these problems. Usually, solutions involve open-ended iterative methods that often have no guaranteed convergence and require a good initial guess. Examples of these methods include the method of homotopy, multipleshootingcombinedwithNewton’siteration,andavarietyof other techniques [1]. Evenformanyproblemswithknownsolutions,implicitequations must be solved iteratively to satisfy the 2BVP. In the two-body problem, this situation occurs in finding a solution to Lambert’s problem, which involves iteration [2,3]. Guibout and Scheeres outlined a novel approach for solving 2BVPs usinggenerating functionsfor canonicaltransformations [4]. Their approach requires the system to be a Hamiltonian dynamical system and relies on solving the Hamilton–Jacobi equation, which has its base in Hamilton’s principle. When a perturbation is present, the solution to the nominal problem isno longer valid (althoughit canbe used as an initial guess to an iterative method), and one must resort to numerical methods. Conventional solutions to 2BVPs involve numerical integration schemesandopen-endediterativesolutions.Thesetypesofsolutions focus on finding an optimal transfer cost around the vicinity of the nominalsolution.Moreover,withsuchanapproach,onecouldeasily find the needed correction to the initial impulse in order to hit the desired target. However, this technique will not portray an accurate description of the system and its behavior. It will concentrate on one target point and find the best solution. While in practice this is desirable, it does not obtain a detailed analysis of the vicinity of the desired solution. Guibout and Scheeres [4] also suggested using Hamilton’s principal function (HPF) to solve the 2BVP for the two-body problem. This function is derived directly from Hamilton’s principle and yields solutions to the equations of motion through “simple differentiations and eliminations” [5]. Although the generating function of the canonical transformation and HPF have different physical significance, they are intimately related. HPF allows the initial and final endpoints and times to be dynamic; that is, they are free to change without affecting the structure of the function. Generating functions, on the other hand, has static initial conditions, viewed as constants of motion, with only the final endpoints being dynamic. In this paper, an analytical perturbation technique is developed, and it solves the 2BVP of a perturbed system using HPF. This technique finds its applications in the two-body problem, configuration of spacecraft formations, optimal control problems, and a variety of problems in astrodynamics and other areas as well. This theory is applied to the problem of two bodies, and it can be used to obtain the solution to the system under perturbing forces. For the nominal two-body 2BVP, Lambert’s problem can be solved iteratively in order to obtain desired solutions; therefore, the solution to these types of problems is well established and generally straightforward. Using analytical expressions developed by the perturbation theory developed in this paper allows one to obtain a closed-form solution for the perturbed Lambert’s problem. Therefore, a family of solutions in the vicinity of the desired target can be obtained. This fact helps us better understand the dynamics of the system, even when perturbing forces are present. Solutions to the perturbed system are obtained by analytically expanding HPF around the nominal solution using a small parameter.

Simulating the Formation of Molecular Clouds. I. Slow Formation by Gravitational Collapse from Static Initial Conditions

We study the formation of H2 in the ISM, using a modified version of the astrophysical magnetohydrodynamical code ZEUS-MP that includes a nonequilibrium treatment of the formation and destruction of H2. We examine two different approximations to treat the shielding of H2 against photodissociation: a local approximation, which gives us a solid lower bound on the amount of shielding, and a method based on ray-tracing that is considerably more accurate in some circumstances but that produces results that are harder to clearly interpret. In both cases, the computational cost of determining H2 photodissociation rates is reduced by enough to make three-dimensional high-resolution simulations of cloud formation feasible with modest computational resources. Our modification to ZEUS-MP also includes a detailed treatment of the thermal behavior of the gas. In this paper, we focus on the problem of molecular cloud formation in gravitationally unstable, initially static gas. (In a subsequent paper, we consider turbulent flow.) We show that in these conditions, and for initial densities consistent with those observed in the cold, neutral atomic phase of the interstellar medium, H2 formation occurs on a timescale t ≥ 10 Myr, comparable to or longer than the gravitational free-fall timescale of the cloud. We also show that the collapsing gas very quickly reaches thermal equilibrium and that the equation of state of the thermal equilibrium gas is generally softer than isothermal. Finally, we demonstrate that although these results show little sensitivity to variations in most of our simulation parameters, they are highly sensitive to the assumed initial density ni. Reducing ni significantly increases the cloud formation timescale and decreases the amount of hydrogen ultimately converted to H2.

Construction and Validation of a Dense Gas Shock Tube

Results from initial tests of a shock tube designed to verify the nonclassical dynamics of Bethe-Zel'dovich-Thompson (BZT) fluids are presented. These tests employed nitrogen at pressures and temperatures required for shock-tube initial conditions that will produce nonclassical phenomena in a BZT fluid. A single-diaphragm, stainless steel shock tube is enclosed in a resistance-heated tube furnace. Each of the 16 segments of the furnace is controlled by a proportional integral differential loop to sustain a uniform temperature along the tube. Water-cooled static and dynamic pressure transducers and thermocouples are used to monitor the static initial conditions and the dynamic wave field. The nitrogen test cases are compared to the ideal gas Riemann problem. The pressure differential of the incident expansion wave matches the theoretical magnitude to within 2%, whereas the average wave speed agrees within 7%

Gravitational collapse in Weyl integrable spacetimes

Spherically symmetric gravitational collapse in Weyl integrable spacetime is studied by some simplified models. The matter content is represented by a perfect fluid coupled with the geometric scalar field. A family of analytical solutions is found for a non-radiative collapsing nebulae of dust and the condition for black hole formation is established. Junction conditions with an exterior spacetime and the radiative collapse of a spherical star are also studied. In this case we find two classes of solutions with an exterior Vaidya spacetime: one with no internal heat flux while the other is obtained from a static initial condition.

Design sensitivity analysis of dynamic systems using Hamilton's law of varying action

Hamilton's law of varying action (HLVA) is used to compute design sensitivity of dynamic systems. The state variables and their variations are approximated using truncated linear sums of orthogonal polynomials and the integral equations are converted to algebraic equations. The orthogonal properties of these polynomials are utilized to make these algebraic equations sparse and thus computationally efficient. This formulation leads to a reduction on the continuity requirement on the states. Four examples are solved to demonstrate the efficacy of this method. Methods to include the state sensitivity to static initial conditions are presented. For comparison, the problems are also solved using the Runge-Kutta integration scheme. Good agreement is found between the two techniques.