Interfacial wave theory of dendrite growth: global mode solution and quantum condition

1990 ◽  
Vol 68 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Turning Point ◽  
Leading Edge ◽  
Wave Theory ◽  
Dendrite Growth ◽  
Interfacial Wave ◽  
Global Mode ◽  
Dendritic Crystal ◽  
Significant Step ◽  
Mode Solution ◽  
Quantum Condition

This paper is concerned with the global mode solutions of dendritic crystal growth. In this paper, we investigate the signal feed-back process at the leading edge of the dendrite tip and derive the global instability mechanism of the system on the basis of the previous results (Phys. Rev. A, 40, 1599 (1989); 40, 1609 (1989)). A global wave diagram of the system is explored, which we call WEASR (Wave emission at the turning point and signal reflections between the turning point and the leading edge of the tip). This WEASR mechanism determines a discrete set of unstable global modes for the system. The asymptotic solutions for these modes and the quantum condition for the corresponding eigenvalues are obtained. The discovery of the WEASR mechanism is quite a significant step leading to the understanding of instability phenomena in dendrite growth.

scholarly journals An application of the interfacial wave theory of solidification

1991 ◽  
Vol 69 (11) ◽  
pp. 1326-1333
Author(s):  
Andonowati Andonowati
Keyword(s):  
Crystal Growth ◽  
Thermal Diffusivity ◽  
Solid State ◽  
Eigenvalue Problem ◽  
Stable State ◽  
Wave Theory ◽  
Interfacial Wave ◽  
Dendritic Crystal ◽  
Linear Eigenvalue Problem ◽  
Quantum Condition

In this paper we apply the interfacial wave theory of dendritic crystal growth to the case in which the thermal diffusivity constant and the specific heat of the liquid state are different from those of the solid state. The problem is formulated as a linear eigenvalue problem. A quantum condition for the eigenvalues is derived and a discrete set of possible solutions is found. The selection problem is solved using the global neutral stable state analysis proposed by the interfacial wave theory.

Self-Acceleration in the Parameterization of Orographic Gravity Wave Drag

2010 ◽  
Vol 67 (8) ◽  
pp. 2537-2546 ◽  
Author(s):  
John F. Scinocca ◽  
Bruce R. Sutherland
Keyword(s):  
Gravity Wave ◽  
Middle Atmosphere ◽  
Wave Train ◽  
Leading Edge ◽  
Wave Theory ◽  
Wave Drag ◽  
Tuning Parameter ◽  
Mean Flow ◽  
Propagating Waves ◽  
The Impact

Abstract A new effect related to the evaluation of momentum deposition in conventional parameterizations of orographic gravity wave drag (GWD) is considered. The effect takes the form of an adjustment to the basic-state wind about which steady-state wave solutions are constructed. The adjustment is conservative and follows from wave–mean flow theory associated with wave transience at the leading edge of the wave train, which sets up the steady solution assumed in such parameterizations. This has been referred to as “self-acceleration” and it is shown to induce a systematic lowering of the elevation of momentum deposition, which depends quadratically on the amplitude of the wave. An expression for the leading-order impact of self-acceleration is derived in terms of a reduction of the critical inverse Froude number Fc, which determines the onset of wave breaking for upwardly propagating waves in orographic GWD schemes. In such schemes Fc is a central tuning parameter and typical values are generally smaller than anticipated from conventional wave theory. Here it is suggested that self-acceleration may provide some of the explanation for why such small values of Fc are required. The impact of Fc on present-day climate is illustrated by simulations of the Canadian Middle Atmosphere Model.

Interfacial wave theory for oscillatory finger formation in a Hele–Shaw cell: a comparison with experiments

1996 ◽  
Vol 7 (2) ◽  
pp. 169-199 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Wave Theory ◽  
Quantitative Agreement ◽  
Instability Mechanism ◽  
Interfacial Wave ◽  
Wave Instability ◽  
Viscous Fingers ◽  
Theoretical Predictions ◽  
Finger Tip ◽  
Hele Shaw Cell ◽  
Comparison With Experiments

This paper is devoted to an analysis of the formation of oscillatory viscous fingers in a Hele-Shaw cell on the basis of the interfacial wave theory, previously established for the pattern formation dynamics in dendrite growth, as well as in the classic Saffman–Taylor flow. In particular, we study the problem of selection and persistence of oscillatory fingers with a tiny bubble at the finger tip. We obtain uniformly valid asymptotic solutions for this problem, and derive the linear, global wave instability mechanism for this more complicated system. The global, neutrally stable modes are computed in a large region of parameters, which select the form of oscillatory fingers in the later stage of evolution. We have compared the theoretical predictions with the experimental data by Couder et al. (1986) and by Kopf-Sill & Homsy (1987), and found excellent quantitative agreement.

scholarly journals Competing Marxist Theories on the Temporal Aspects of Strike Waves: Silver’s Product Cycle Theory and Mandel’s Long Wave Theory

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Eddie Cottle
Keyword(s):  
South African ◽  
Turning Point ◽  
Industrial Revolution ◽  
Explanatory Power ◽  
Wave Theory ◽  
Product Cycle ◽  
The South ◽  
Capitalist Development ◽  
Long Wave ◽  
Temporal Aspects

Despite the profound changes in capitalist development since the industrial revolution, strike waves and mass strikes are still a feature of the twenty-first century. This article examines two Marxist theories that seek to explain the temporal aspects of strike waves. In the main, I argue that Silver’s product cycle theory, suffers from an over-determinism, and that turning point strike waves are not mainly determined by lead industries. Mandel’s long wave theory argues that technological innovations tend to cluster and thus workers in different industries feature prominently in strike waves. By re-examining and comparing two competing Marxist theories on the temporality of strike waves and turning points, I will attempt to highlight the similarities but also place emphasis on where the theories differ. I examine the applicability of the theories to the South African case, and reference recent world events in order to ascertain the explanatory power of the competing theories. In the main I argue that Silver’s product cycle lead theory does not fit the South African experience. KEYWORDS  turning point strike waves; product cycle; long waves; capitalism

scholarly journals A quantum Hopfield associative memory implemented on an actual quantum processor

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nathan Eli Miller ◽  
Saibal Mukhopadhyay
Keyword(s):  
Machine Learning ◽  
Quantum Computing ◽  
Associative Memory ◽  
Leading Edge ◽  
Memory Capacity ◽  
Quantum Processor ◽  
Significant Step ◽  
Machine Learning Applications ◽  
Noise Models ◽  
Ibm Quantum Experience

AbstractIn this work, we present a Quantum Hopfield Associative Memory (QHAM) and demonstrate its capabilities in simulation and hardware using IBM Quantum Experience.. The QHAM is based on a quantum neuron design which can be utilized for many different machine learning applications and can be implemented on real quantum hardware without requiring mid-circuit measurement or reset operations. We analyze the accuracy of the neuron and the full QHAM considering hardware errors via simulation with hardware noise models as well as with implementation on the 15-qubit ibmq_16_melbourne device. The quantum neuron and the QHAM are shown to be resilient to noise and require low qubit overhead and gate complexity. We benchmark the QHAM by testing its effective memory capacity and demonstrate its capabilities in the NISQ-era of quantum hardware. This demonstration of the first functional QHAM to be implemented in NISQ-era quantum hardware is a significant step in machine learning at the leading edge of quantum computing.

Receptivity and sensitivity of the leading-edge boundary layer of a swept wing

2015 ◽  
Vol 775 ◽  
Author(s):  
Gianluca Meneghello ◽  
Peter J. Schmid ◽  
Patrick Huerre
Keyword(s):  
Boundary Layer ◽  
Flow Instability ◽  
Cross Flow ◽  
Leading Edge ◽  
Open Loop ◽  
Base Flow ◽  
Local Instability ◽  
Swept Wing ◽  
Global Mode ◽  
Attachment Line

A global stability analysis of the boundary layer in the leading edge of a swept wing is performed in the incompressible flow regime. It is demonstrated that the global eigenfunctions display the features characterizing the local instability of the attachment line, as in swept Hiemenz flow, and those of local cross-flow instabilities further downstream along the wing. A continuous connection along the chordwise direction is established between the two local eigenfunctions. An adjoint-based receptivity analysis reveals that the global eigenfunction is most responsive to forcing applied in the immediate vicinity of the attachment line. Furthermore, a sensitivity analysis identifies the wavemaker at a location that is also very close to the attachment line where the corresponding local instability analysis holds: the local cross-flow instability further along the wing is merely fed by its attachment-line counterpart. As a consequence, global mode calculations for the entire leading-edge region only need to include attachment-line structures. The result additionally implies that effective open-loop control strategies should focus on base-flow modifications in the region where the local attachment-line instability prevails.

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