scholarly journals Расчет динамики границы аморфная фаза-кристалл при твердофазной взрывной кристаллизации

2021 ◽  
Vol 63 (11) ◽  
pp. 1927
Author(s):  
А.А. Чеврычкина ◽  
Н.М. Бессонов ◽  
А.Л. Корженевский
Keyword(s):  
Differential Equation ◽  
Constant Velocity ◽  
Solid Phase ◽  
Crystallization Front ◽  
The Self ◽  
Mode Transition ◽  
Explosive Crystallization ◽  
Theoretical Results ◽  
Front Motion ◽  
Oscillating Mode

The nonlinear differential equation described a dynamics of solid-phase explosive crystallization front in a much larger parameters domain in comparison with the theoretical results available in literature was obtained. The features of the self-oscillating mode transition of the front motion to the mode of its self-propagation with a constant velocity was numerically studied in detail.

Uniform and Directed Crystallization of Deposited a­Si on Glass Substrates at Linear Velocities Of 1 to 20 Meters Per Second

1981 ◽  
Vol 4 ◽  
Author(s):  
D. Bensahel ◽  
G. Auvert ◽  
V. T. Nguyen ◽  
G. A. Rozgonyi
Keyword(s):  
Phase Boundary ◽  
Laser Power ◽  
Crystallization Process ◽  
Solid Phase ◽  
Crystallization Front ◽  
Continuous Furnace ◽  
Directed Crystallization ◽  
Glass Substrates ◽  
Explosive Crystallization ◽  
Scan Speed

ABSTRACTIt has been found that careful control of the laser power and scan speed will convert deposited a­Si into continuous lines of uniformly crystallized silicon. Two solid phase “explosive” crystallization front velocities of 1000 cm/sec and 1400 cm/sec have been experimentally determined by matching the laser scan velocity with the runaway a–c phase boundary. If solid phase explosive crystallization is suppressed by pre-annealing, then a liquid assisted runaway crystallization velocity of 220 cm/sec is observed, as well as a continuous furnace-like crystallization process at 250 cm/sec.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

Study of the Effect of Hole Clearance and Thread Fit on the Self-Loosening of Threaded Fasteners

2006 ◽  
Vol 129 (6) ◽  
pp. 586-594 ◽  
Author(s):  
Sayed A. Nassar ◽  
Basil A. Housari
Keyword(s):  
Analytical Investigation ◽  
The Self ◽  
Time Data ◽  
Experimental Procedure ◽  
Test Setup ◽  
Threaded Fasteners ◽  
Service Load ◽  
Real Time Data ◽  
Theoretical Results ◽  
Simplified Mathematical Model

This study provides an experimental and theoretical investigation of the effect of hole clearance and thread fit on the self-loosening of tightened threaded fasteners that are subjected to a cyclic transverse service load. An experimental procedure and test setup are developed in order to collect real-time data on the rate of clamp load loss per cycle as well as the loosening rotation of the bolt head. Three levels of hole clearance are investigated; namely, 3%, 6%, and 10% of the bolt nominal diameter. For the commonly used 2A thread fit for a selected bolt size, three classes of the nut thread fit are considered; namely, 1B, 2B, and 3B. A simplified mathematical model is used for the analytical investigation of the effect of the hole clearance and thread fit on threaded fasteners self-loosening. The experimental and theoretical results are presented and discussed.

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

Calculating Method for the Solid Phase Effect Coefficient of the Solid-Fluid Two Phase Flow Centrifugal Pump

2010 ◽  
Vol 29-32 ◽  
pp. 658-663
Author(s):  
Chuan Jun Li ◽  
Gang Yu ◽  
Xin Wang
Keyword(s):  
Differential Equation ◽  
Centrifugal Pump ◽  
Two Phase Flow ◽  
Solid Phase ◽  
High Accuracy ◽  
Phase Flow ◽  
Phase Effect ◽  
Two Phase ◽  
Error Band ◽  
Calculating Method

In order to acquire the solid-fluid two phase flow centrifugal pump’s slurry head according with the fact, the solid phase effect coefficient must be calculated precisely. By analysising the acting forces on the solid particle, its moving differential equation was established. And the calculating formula of the solid phase effect coefficient was deduced based on the equation. For the sake of verifying its validity, a test of contrast and comparison on the calculating slurry heads by some ways was carried out. The results shows that the relative error values of the slurry head calculated are less than 2.00% with a small and stably error band. The method has the advantage of simple calculating process, high accuracy, low randomness and good practicability.

SELF-ADAPTING FAÇADE SYSTEMS: EXPERIMENTATION REGARDING THE EXPLOITATION OF THERMAL DILATION

2020 ◽  
Vol 15 (4) ◽  
pp. 67-90
Author(s):  
Livio Petriccione ◽  
Fabio Fulchir ◽  
Francesco Chinellato
Keyword(s):  
Environmental Temperature ◽  
State Of The Art ◽  
The Self ◽  
External Energy ◽  
Building Envelopes ◽  
Orientation System ◽  
Thermal Dilation ◽  
Theoretical Results ◽  
Productive Development ◽  
Critical Aspects

ABSTRACT An original and innovative solar device orientation system is illustrated, together with the results of research and experimentation. The system proposed uses only the force generated by natural thermal dilation, without the help of motors, computerized devices or external energy sources, thus overcoming some critical aspects of the self-adaptive type of building envelopes used up until now. In the course of the research a mathematical model was developed to correlate the variation of the environmental temperature with the consequent expansion of the dilating elements of the system. The results of the tests carried out confirmed an excellent correspondence between the theoretical results and the experimentation. The state of the art of the research has all its theoretical aspects defined and some partial prototypes created. It is planned to build some complete prototypes with the realistic prospect of productive development.

scholarly journals Generalization of the Unified Analytic Melt-Shear Model to Multi-Phase Materials: Molybdenum as an Example

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 86 ◽  
Author(s):  
Leonid Burakovsky ◽  
Darby Luscher ◽  
Dean Preston ◽  
Sky Sjue ◽  
Diane Vaughan
Keyword(s):  
Shear Modulus ◽  
Solid Phase ◽  
Model Parameters ◽  
Quantum Molecular Dynamics ◽  
Face Centered Cubic ◽  
Shear Model ◽  
Bcc Structure ◽  
Face Centered ◽  
Multi Phase ◽  
Theoretical Results

The unified analytic melt-shear model that we introduced a decade ago is generalized to multi-phase materials. A new scheme for calculating the values of the model parameters for both the cold ( T = 0 ) shear modulus ( G ) and the melting temperature at all densities ( ρ ) is developed. The generalized melt-shear model is applied to molybdenum, a multi-phase material with a body-centered cubic (bcc) structure at low ρ which loses its dynamical stability with increasing pressure (P) and is therefore replaced by another (dynamically stable) solid structure at high ρ . One of the candidates for the high- ρ structure of Mo is face-centered cubic (fcc). The model is compared to (i) our ab initio results on the cold shear modulus of both bcc-Mo and fcc-Mo as a function of ρ , and (ii) the available theoretical results on the melting of bcc-Mo and our own quantum molecular dynamics (QMD) simulations of one melting point of fcc-Mo. Our generalized model of G ( ρ , T ) is used to calculate the shear modulus of bcc-Mo along its principal Hugoniot. It predicts that G of bcc-Mo increases with P up to ∼240 GPa and then decreases at higher P. This behavior is intrinsic to bcc-Mo and does not require the introduction of another solid phase such as Phase II suggested by Errandonea et al. Generalized melt-shear models for Ta and W also predict an increase in G followed by a decrease along the principal Hugoniot, hence this behavior may be typical for transition metals with ambient bcc structure that dynamically destabilize at high P. Thus, we concur with the conclusion reached in several recent papers (Nguyen et al., Zhang et al., Wang et al.) that no solid-solid phase transition can be definitively inferred on the basis of sound velocity data from shock experiments on Mo. Finally, our QMD simulations support the validity of the phase diagram of Mo suggested by Zeng et al.

The Investigation of a Fluid-Solid Interaction Mathematical Model under Combined Convective Jeffrey Flow and Radiation Effect Embedded Newtonian Heating as the Thermal Boundary Condition over a Vertical Stretching Sheet

2020 ◽  
Vol 399 ◽  
pp. 65-75 ◽  
Author(s):  
Abdul Rahman Mohd Kasim ◽  
Nur Syamilah Arifin ◽  
Syazwani Mohd Zokri ◽  
Mohd Zuki Salleh
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Stretching Sheet ◽  
Solid Phase ◽  
Particle Interaction ◽  
Thermal Boundary Condition ◽  
Dust Particles ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Newtonian Heating

The investigation on the interaction between solid and fluid under combined convective flow has been carried out mathematically. The Jeffrey fluid model is taken as the fluid phase and the model is being embedded with the dust particles (solid phase). This two-phase model is constructed by introducing the fluid-particles interaction forces in the momentum equations of the fluid and dust phases, respectively. The natural and forced convections together with the aligned magnetic field are considered on the fluid flow. Also, the Newtonian heating as thermal boundary condition is induced on the vertical stretching sheet. In order to reduce the complexity of the model, the governing equations are transformed from partial differential equation into ordinary differential equation via suitable similarity transformation. The solutions are obtained in terms of velocity and temperature profiles for the fluid and particles phases respectively whereby the Keller-box method is utilized to obtain the desired outcomes. The influences of several significant physical parameters are visualized graphically to clarify the flow and heat transfer characteristic for both phases. The investigation found that the fluid’s velocity is affected by the presence of the dust particles which led to decelerate the fluid transference. The present flow model is able to be compared with the single-phase fluid cases if the fluid-particle interaction parameter is ignored.

Optimization Design of Self-Balacing Torsion Bar Diameter

2011 ◽  
Vol 308-310 ◽  
pp. 2486-2489
Author(s):  
Zhi Qi Huang
Keyword(s):  
Optimization Model ◽  
Optimization Design ◽  
Ant Colony Algorithm ◽  
The Self ◽  
Ant Colony ◽  
New Method ◽  
C Language ◽  
Torsion Bar ◽  
Bar Diameter ◽  
Theoretical Results

The thesis builds the optimization model for the self-balacing torsion bar, On the basis of the Ant Colony Algorithm, designs the Ant Colony Algorithm procedure using C Language and optimizes torsion bar diameter. Results show the Ant Colony Algorithm is feasible and provides a new method choosing torsion bar diameter. The max difference value is 1.12% between optimizing results and theoretical results.

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

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