Set Of Scaling Laws Research Articles

A SCALING LAW FOR THE COSMOLOGICAL CONSTANT FROM A STOCHASTIC MODEL FOR COSMIC STRUCTURES

A set of scaling laws, based on the stochastic motions of the granular components of astronomical systems, is applied to a cosmological model with a positive cosmological constant. It follows that the mass of the dominant particle in the observable universe must be proportional to the sixth root of the cosmological constant and of order near the nucleon mass, which is consistent with the Zel'dovich scaling law. The approach is a natural way to solve the "cosmic coincidence" problem. On the other hand, the observed value of the cosmological constant emerges as the result of a scaling law induced by the stochastic mechanism which gives rise to the gravitationally bound systems.

Mathematical formulation to predict the harmonics of the superconducting Large Hadron Collider magnets. II. Dynamic field changes and scaling laws

A superconducting particle accelerator like the LHC (Large Hadron Collider) at CERN, can only be controlled well if the effects of the magnetic field multipoles on the beam are compensated. The demands on a control system solely based on beam feedback may be too high for the requirements to be reached at the specified bandwidth and accuracy. Therefore, we designed a suitable field description for the LHC (FIDEL) as part of the machine control baseline to act as a feed-forward magnetic field prediction system. FIDEL consists of a physical and empirical parametric field model based on magnetic measurements at warm and in cryogenic conditions. The performance of FIDEL is particularly critical at injection when the field decays, and in the initial part of the acceleration when the field snaps back. These dynamic components are both current and time dependent and are not reproducible from cycle to cycle since they also depend on the magnet powering history. In this paper a qualitative and quantitative description of the dynamic field behavior substantiated by a set of scaling laws is presented.

The large number coincidence, the cosmic coincidence and the critical acceleration

The coincidence problem among the pure numbers of order near 10 40 is resolved with the Raychaudhuri and Friedmann–Robertson–Lemaitre–Walker equations and a trivial relationship involving the fine structure constant. The fact that the large number coincidence occurs only in the same epoch in which other coincidences among cosmic parameters occur could be considered a distinct coincidence problem suggesting an underlying physical connection. A natural set of scaling laws for the cosmological constant and the critical acceleration is identified that would resolve the coincidence among cosmic coincidences.

Observations of Water Vapor Outflow from NML Cygnus

We report new observations of the far-infrared and submillimeter water vapor emission of NML Cygnus based on data gathered with the Infrared Space Observatory and the Submillimeter Wave Astronomy Satellite. We compare the emission from NML Cyg to that previously published for VY CMa and W Hya in an attempt to establish the validity of recently proposed models for the outflow from evolved stars. The data obtained support the contention by Ivezic & Elitzur that the atmospheres of evolved stars obey a set of scaling laws in which the optical depth of the outflow is the single most significant scaling parameter, affecting both the radiative transfer and the dynamics of the outflow. Specifically, we provide observations comparing the water vapor emission from NML Cyg, VY CMa, and W Hya and find, to the extent permitted by the quality of our data, that the results are in reasonable agreement with a model developed by Zubko & Elitzur. Using this model we derive a mass loss based on the dust opacities, spectral line fluxes, and outflow velocities of water vapor observed in the atmospheres of these oxygen-rich giants. For VY CMa and NML Cyg, we also obtain an estimate of the stellar mass.

System characteristics of quasi-optical power amplifiers

Quasi-optical (QO) amplifiers have advanced to the point where they are competitive with other solid state and vacuum-based power amplifier technologies in the upper microwave and millimeter-wave bands. While still trailing in power-added efficiency, the QO amplifiers have advantages over traditional system architectures because of superior linearity, low noise, high spurious-free dynamic range, and added functionality (e.g., electronic beam steering). These advantages are stated in the present paper through a set of scaling laws that describe the behavior of fundamental amplifier properties versus the number n of elements in the QO array. It is known that the gain and power-added efficiency are scale independent, so that the output power scales as n/sup 1/. Here we find that the white noise figure is scale independent and the 3rd order intercept point increases as n/sup 3/2/. Hence, the spurious-free dynamic range (SFDR) should scale as n/sup 1/.. This makes QO amplifiers attractive as robust low-noise amplifiers (LNAs) in traditional superheterodyne receivers. An analysis is carried out to predict the improvement in total SFDR of a superheterodyne receiver having a QO LNA at the front end.

Flux-canceling electrodynamic maglev suspension. II. Test results and scaling laws

Electrodynamic suspensions (EDS) are highly undamped and require some form of active control or a secondary suspension to achieve adequate ride quality. This paper reports on efforts to develop a version of EDS that uses controllable magnetic forces to eliminate the need for any secondary suspension. The magnetic forces act directly on the guideway and avoid the need to have unsprung weight and a secondary suspension. It is shown that the energy required to effect this control can be less than 1% of the energy stored in the suspension magnets, so a modest size controller can be used. The same controller can also provide lift at very low speeds and thereby eliminate the need for a separate low-speed suspension system. A set of scaling laws is described which is used to size a full-scale high-temperature superconductor (HTSC)-based suspension magnet. The test fixture was also used to verify the use of zero velocity lift, where ac excitation is used in the suspension coils to achieve lift at low train velocity.

Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach is derived from the Reynolds averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k–∈ model are not consistent with most of the new turbulent scaling laws.

Scaling Formulas for Deuterium-Deuterium Neutron Emission in JET

An heuristic approach has been adopted to obtain empirical scaling formulas for the dependence of neutron emission on predefined machine parameters, such as applied auxiliary heating power, plasma current IP, and toroidal magnetic field BT. The results are intended to be used to predict the neutron emission before each discharge. These formulas are of interest in their own right but more practically can be used as input to control software to pre-set the optimum precollimator apertures for neutron diagnostics such as spectrometers. Formulas have been obtained for data from plasma pulses during the years 1992 and (1994 + 1995), i.e., before and after the divertor installation and major modifications of the Joint European Torus (JET) vessel.Obtained scaling formulas for moderate beam power PNB show neutron emission after installation of the divertor to be lower than before. However, for high beam power, the scaling laws predict as large and even larger neutron emissions for the (1994 + 1995) neutral beam (NB)-heated plasmas as compared to 1992 plasmas. The dependence on radio-frequency (rf) heating power Prf is significantly larger in the scaling laws deduced prior to the divertor phase than after, which implies more efficient heating in 1992. With the exception of combined NB- and rf-heated plasma pulses, the dependence on plasma current has increased moderately after the modifications of JET. For all observations with combined NB and rf heating, the dependence on Prf is quite small, and the neutron production for this category of discharges is dominated by NB heating.A set of scaling laws is found that predicts the neutron emission within a factor of 2, which is consistent with our objective.

Structural similitude for vibration response of laminated cylindrical shells with double curvature

In order to understand the applicability of scaled down models in designing laminated composite structures, an analytical investigation was undertaken to assess the feasibility of their use. Employment of similitude theory to establish similarity among structural systems can save considerable expense and time, provided the proper scaling laws are found and validated. The developed methodology is demonstrated through application of similitude theory to laminated cylindrical shells. Particular emphasis is placed on the case of free vibration of cross-ply laminated cylindrical shells with double curvature. The results presented herein indicate that, for free vibration responses of laminated cylindrical shells of double curvature, based on structural similitude, a set of scaling laws can be found which are used to develop design rules for designing small scale models. This analytical study indicates that distorted models with a different number of layers, geometries and material properties than those of the prototype can predict the behavior of the prototype with good accuracy. However, it is shown that a scaled down model with distorted curvature is incapable of predicting the response of the prototype.

Mean-velocity scaling in and around a mild, turbulent separation bubble

This paper examines the question of the scaling of mean-velocity profiles in adverse-pressure-gradient flows. In these flows, the mean velocity scaling must be different than in zero-pressure-gradient flows, because the friction velocity used in the latter case can become vanishingly small in the former. Two decades ago, Perry and Schofield [Phys. Fluids 16, 2068 (1973)] proposed a new outer-region scaling law to be used when the boundary layer approaches separation. Since that time, a number of sets of experimental data close to separation have been shown to fall on a universal curve when the profiles are plotted in Perry–Schofield coordinates, and the profile shape was given by Dengel and Fernholz [J. Fluid Mech. 212, 615 (1990)]. Recently, however, a new set of scaling laws has been proposed by Durbin and Belcher [J. Fluid Mech. 238, 699 (1992)] as a result of their asymptotic analysis, in which they assumed the appropriate near-wall velocity scale to be based on the local strength of the pressure gradient. The resulting scaling laws are different than Perry and Schofield’s scaling and, in fact, predict a three-layered rather than a two-layered boundary-layer structure. Here, experimental results are shown for an adverse-pressure-gradient boundary layer which separates from and then reattaches to a smooth surface. These data provide a wide range of flow conditions for comparing the conflicting scaling laws mentioned above, under conditions of both decreasing and increasing skin friction, with and without instantaneous reverse flow. It is found that the Perry–Schofield coordinates provide better collapse, over a wider range of streamwise positions and over a larger fraction of the boundary layer, than the scaling laws of Durbin and Belcher. Other proposed scaling laws are also evaluated. Yaglom’s half-power law is shown to hold for a subset of the profiles which fall on Dengel and Fernholz’s universal profile. And the data provide a test of the range of validity of the (zero-pressure-gradient) logarithmic law of the wall. The law is violated here when instantaneous reverse flow exists in the boundary layer and/or when the local pressure gradient is strong enough, as is consistent with earlier work. However, after reattachment these criteria are insufficient to indicate the return to the log law, and several bubble lengths are required after reattachment before the universal log law is satisfied. The wake region responds to reattachment more slowly and does not appear fully recovered six bubble lengths (twenty boundary-layer thicknesses) after reattachment.

Scaling Laws for Fatigue Crack Growth of Large Cracks in Steels

A set of scaling laws has been developed for describing intermittent as well as continuous fatigue crack growth of large cracks in steels in the power-law regime. The proposed scaling laws are developed on the basis that fatigue crack growth occurs as the result of low-cycle fatigue (LCF) failure of a crack-tip element whose width and height correspond to the dislocation cell size and barrier spacing, respectively. The results show that the effects of microstructure on fatigue crack growth can be described entirely in terms of a dimensionless microstructural parameter, ξ, which is defined in terms of yield stress, fatigue ductility, dislocation cell size, and dislocation barrier spacing. For both discontinuous and continuum crack growth, the crack extension rate,da/dN, scales with ξ and(ΔK/E) m, where ΔK is the stress intensity range, m is the crack growth exponent, andE is Young's modulus. Application of the model to high-strength low-alloy (HSLA) and conventional ferritic, ferritic/pearlitic, and martensitic steels reveals that the lack of a strong microstructural influence on fatigue crack growth in the power-law regime is due to increasing yield stress and fatigue ductility with decreasing dislocation barrier spacing, which leads to a narrow range of ξ values and crack growth rates. Variation ofda/dN data with microstructure in HSLA-80 steels is explained in terms of the proposed model. Other implications of the scaling laws are also presented and discussed in conjunction with several fatigue models in the literature.

The theory of magnetohydrodynamic wave generation by localized sources. III - Efficiency of plasma heating by dissipation of far-field waves

The fraction of radiation emitted by Alfven waves is calculated by using two separate methods to determine whether the Alfven flux generated in the photosphere is sufficient to heat the corona. One method employs a set of scaling laws for the fluxes as functions of plasma and source parameters; the second method consist of a procedure for calculating the flux in each waveband from the interaction of vector-harmonic components of an arbitrary applied forcing. Both methods indicate that the Alfven flux accounts roughly for half of the total emission. The need to reexamine estimates of the amount of Alfven flux reaching the corona based on observations of plasma disturbances in the photosphere is emphasized.

Scaling laws for testing airfoils under heavy rainfall

Subscale test data have shown that airfoils operating in a simulated heavy-rain environment can experience significant performance penalties. The physical mechanism resulting in this performance penalty has yet to be conclusively identified. Therefore, the extrapolation of subscale data to full-scale conditions must be undertaken with extreme caution since complete scaling laws are unknown. This paper discusses some of the technical issues that must be addressed and resolved prior to extrapolating the performance of full-scale airfoils from subscale test data. A set of scaling laws is suggested based on the neglect of thermodynamic interactions between the droplets and the air/water vapor phase.

The evolution of plastic resistance in large strain plastic flow of single phase subgrain forming metals

A detailed dislocation model is developed for the evolution of plastic resistance to large strain monotonie deformation of polycrystalline single phase, subgrain forming cubic metals. The model is based on a cellular dislocation structure with different but interactive evolutionary laws existing for the cell interiors and the cell walls, under conditions of continued similitude, holding separately for the two components. Strain hardening processes are considered to be statistical and diffuse, while recovery is assumed to be of a dynamic nature inside the cells and static nature in the cell walls. Comparison of the model with the experimental results of Lloyd et al. on aluminum alloys gives very satisfactory agreement and can be taken as demonstration of the utility of the development as a set of scaling laws.

On the Scaling Laws for Air Clearing in Water-Type Pressure Suppression Systems

A set of scaling laws is derived for the small-scale simulation of the air clearing phase of a loss-of-coolant accident in a nuclear powerplant with a water-type pressure suppression system. The laws are a refinement of those suggested by F. J. Moody. This paper discusses the assumptions underlying their derivation and deals with the problem of scaling the vent flow.

Scaling laws applicable to some on-floor duct drying systems

Using a non-linear pressure velocity relation for the flow in a porous medium and the equations describing the pressure field, a set of scaling laws have been derived. These relate the performance of geometrically similar two-dimensional configurations of on-floor duct drying and aeration systems.