Engineering topics

Langer, J. S.

Publications and source records attributed to Langer, J. S..

At least 19 records

NASA NTRS1992

Patterns of seismic activity preceding large earthquakes

A mechanical model of seismic faults is employed to investigate the seismic activities that occur prior to major events. The block-and-spring model dynamically generates a statistical distribution of smaller slipping events that precede large events, and the results satisfy the Gutenberg-Richter law. The scaling behavior during a loading cycle suggests small but systematic variations in space and time with maximum activity acceleration near the future epicenter. Activity patterns inferred from data on seismicity in California demonstrate a regional aspect; increased activity in certain areas are found to precede major earthquake events. One example is given regarding the Loma Prieta earthquake of 1989 which is located near a fault section associated with increased activity levels.

Shaw, Bruce E.↗

NASA NTRS1990

Stability of dendritic arrays

An approximate method for studying steady-state properties and linear stability of the dendritic arrays that are formed in directional solidification of alloys is proposed. This analysis is valid at high growth rates where the primary spacing between dendrites is larger than the velocity-dependent solutal diffusion length. A neutral stability boundary is computed and it is found that, in the situations where the results should be valid, the experimental data of Somboonsuk, et al. (1984) lie in the stable region, well away from the boundary.

Warren, James A.↗

NASA NTRS1989

Mechanical model of an earthquake fault

The dynamic behavior of a simple mechanical model of an earthquake fault is studied. This model, introduced originally by Burridge and Knopoff (1967), consists of an elastically coupled chain of masses in contact with a moving rough surface. The present version of the model retains the full Newtonian dynamics with inertial effects and contains no externally imposed stochasticity or spatial inhomogeneity. The only nonlinear feature is a velocity-weakening stick-slip friction force between the masses and the moving surface. This system is being driven persistently toward a slipping instability and therefore exhibits noisy sequences of earthquakelike events. These events are observed in numerical simulations, and many of their features can be predicted analytically.

Carlson, J. M.↗

NASA NTRS1989

Droplet model for autocorrelation functions in an Ising ferromagnet

The autocorrelation function of Ising spins in an ordered phase is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation which describes fluctuations in the radius of a single droplet is studied in detail. A general description of the transformation to a Fokker-Planck equations and the ways in which a spectral analysis of that equation can be used to compute the autocorrelation function is given. It is shown that the eigenvalues of the Fokker-Planck operator form (1) a continuous spectrum of relaxation rates starting from zero for d = 2, (2) a continuous spectrum with a finite gap for d = 3, and (3) a discrete spectrum for d greater than 4, where d is the spatial dimensionality. Detailed solutions for various cases are presented.

Tang, Chao↗

NASA NTRS1989

Properties of earthquakes generated by fault dynamics

A model for fault dynamics consisting of a uniform chain of blocks and springs pulled slowly across a rough surface is presented. The only nonlinear element of the model is a slip-stick friction force between the blocks and the surface. It is found that this model gives rise to events of all sizes. The numerical evaluation of the distribution of earthquake magnitudes results in a power-law spectrum similar to what is observed in nature. Like certain other dissipative dynamical systems, the observed large fluctuations in earthquake magnitude persist because the system is in a state of marginal stability.

Carlson, J. M.↗

NASA NTRS1989

Predictions of dendritic growth rates in the linearized solvability theory

The velocity-selection phenomenon in dendritic solidification is investigated theoretically. A WKB-type solvability condition is derived which is applicable to two- and three-dimensional symmetric and one-sided models; this condition is then solved numerically to obtain existence conditions for steady-state needle crystals. Numerical results are presented in graphs and discussed with reference to published numerical and experimental data.

Barbieri, A.↗

NASA NTRS1989

Dendrites, viscous fingers, and the theory of pattern formation

Recent developments in the theory of pattern formation in dendritic crystal growth and viscous fingering in fluids are reviewed. Consideration is given to the discovery that weak capillary forces act as singular perturbations which lead to selection mechanisms in dendritic crystal growth and fingering patterns. Other topics include the conventional thermodynamic model of the solidification of a pure substance from its melt, fingering instability, pattern selection, the solvability theory, dendritic growth rates, the bubble effect discovered by Couder et al. (1986), the dynamics of pattern-forming systems, and snowflake formation.

Langer, J. S.↗

NASA NTRS1987

Dynamics of dendritic sidebranching in the two-dimensional symmetric model of solidification

Within a WKB approximation, the evolution of time-dependent deformations of the needle crystal solution of the two-dimensional symmetric model of solidification is studied. It is found that perturbations with fixed small frequencies are initially amplified as they propagate from near the tip down the dendrite but ultimately decay. Localized wave packets behave rather differently; the packet continues to grow exponentially as it moves to arbitrarily large distances from the tip. The relevance of these results to sidebranching of dendrites is discussed.

Barber, Michael N.↗

NASA NTRS1987

Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise

The time-dependent behavior of sidebranching deformations in the three-dimensional symmetric model of dendritic solidification is studied within a WKB approximation. Localized wave packets generated by pulses in the neighborhood of the tip are found to grow in amplitude and to spread and stretch as they move down the sides of the dendrite. This behavior is shown to imply that noise in the solidifying medium is selectively amplified in such a way as to produce a fluctuating train of sidebranches in qualitative agreement with experimental observations. A rough estimate indicates that purely thermal noise is probably not quite strong enough to fit the data.

Langer, J. S.↗

NASA NTRS1987

Pattern selection and tip perturbations in the Saffman-Taylor problem

An analytic approach to the Saffman-Taylor problem of predicting the width of a viscous finger in a Hele-Shaw cell is presented. The first purpose is to provide a systematic description of the way in which the singular perturbation introduced by capillary forces leads to a solvability mechanism for pattern selection. It is then shown how recent experimental observations by Couder et al. (1986) may be interpreted in terms suggested by this mechanism.

Hong, D. C.↗

NASA NTRS1987

Velocity selection in the symmetric model of dendritic crystal growth

An analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth is presented. The analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needle-like solidification fronts in the limit of small under-cooling Delta. For the two-dimensional symmetric model with a capillary anisotropy of strength alpha, it is found that the velocity is proportional to (Delta to the 4th) times (alpha exp 7/4). The application of the method in three dimensions is also described.

Barbieri, Angelo↗

NASA NTRS1986

Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy

This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. The two-dimensional version of this model with a fourfold crystalline anisotropy alpha in the surface tension is considered. By extending a WKB method introduced in an earlier paper, the alpha dependence of the selected growth rate is determined in the limit of small alpha; and this rate is studied for large alphas in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.

Langer, J. S.↗

NASA NTRS1986

Analytic theory of the selection mechanism in the Saffman-Taylor problem

An analytic approach to the problem of predicting the widths of fingers in a Hele-Shaw cell is presented. The analysis is based on the WKB technique developed recently for dealing with the effects of surface tension in the problem of dendritic solidification. It is found that the relation between the dimensionless width lambda and the dimensionless group of parameters containing the surface tension, nu, has the form lambda - 1/2 = nu exp 2/3 in the limit of small nu.

Hong, D. C.↗

NASA NTRS1986

Noise-driven sidebranching in the boundary-layer model of dendritic solidification

In the context of local models of solidification, it is suggested that the sidebranching which appears to be a characteristic feature of dendritic processes may be generated by selective amplification of noise near the tip and that, under some circumstances, thermal fluctuations may be strong enough to explain the observed effects. This proposal is discussed based on the two-dimensional boundary-layer model with kinetic crystalline anisotropy. Experimental methods to distinguish this stochastic process from a deterministic, dynamical sidebranching mechanism are suggested, including the possibility of space-based experiments.

Pieters, R.↗

NASA NTRS1986

Existence of needle crystals in local models of solidification

The way in which surface tension acts as a singular perturbation to destroy the continuous family of needle-crystal solutions of the steady-state growth equations is analyzed in detail for two local models of solidification. All calculations are performed in the limit of small surface tension or, equivalently, small velocity. The basic mathematical ideas are introduced in connection with a quasilinear, isotropic version of the geometrical model of Brower et al., in which case the continuous family of solutions dissappears completely. The formalism is then applied to a simplified boundary-layer model with an anisotropic kinetic attachment coefficient. In the latter case, the solvability condition for the existence of needle crystals can be satisfied whenever the coefficient of anisotropy is arbitrarily small but nonzero.

Langer, J. S.↗

NASA NTRS1986

Solvability condition for needle crystals at large undercooling in a nonlocal model of solidification

It is explicitly shown that, in a realistic model of diffusion-controlled dendritic solidification, Ivantsov's continuous family of steady-state needle crystals is destroyed by the addition of surface tension. The starting point is in the exact integro-differential equation for the one-sided model, in two dimensions, in a moving frame of reference. In the limit of large undercooling, where the range of the diffusion field is much smaller than the radius of curvature of the tip of the needle, this problem is reduced to a linear, inhomogeneous differential equation of infinite order. A solvability condition for this equation is derived and it is shown that solutions cease to exist for arbitrarily small but finite isotropic surface tension.

Caroli, B.↗

NASA NTRS1985

Theoretical Problems in Materials Science

Interactions between theoretical physics and material sciences to identify problems of common interest in which some of the powerful theoretical approaches developed for other branches of physics may be applied to problems in materials science are presented. A unique structure was identified in rapidly quenched Al-14% Mn. The material has long-range directed bonds with icosahedral symmetry which does not form a regular structure but instead forms an amorphous-like quasiperiodic structure. Finite volume fractions of second phase material is advanced and is coupled with nucleation theory to describe the formation and structure of precipitating phases in alloys. Application of the theory of pattern formation to the problem of dendrite formation is studied.

Langer, J. S.↗

NASA NTRS1985

Chiral solidification of a phospholipid monolayer

The formation of chiral solidlike domains observed by Weiss and McConnell (1984) in monolayers of depalmitoylphosphatidylcholine (DPPC) floating on an air-water interface is investigated theoretically. It is proposed that the diffusion tensor for the two-dimensional fluidlike phase of the DPPC molecules has a chiral component acting perpendicular to the concentration gradient and coupled to the rotational motion of a pinwheellike molecule by the viscous forces. Diagrams are provided, and numerical estimates of the forces involved are shown to be in agreement with the observed behavior of the structures.

Langer, J. S.↗