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مقاله مکانیک 6 - خصوصیات دینامیک جامدات - فصل دوم by: امید ترجمان

فصل دوم کتاب " خصوصیات دینامیک جامدات" به مبحث "کاربردهای دینامیک شبکه پتانسیل های موثر متغیر در فرمول بندی انتگرال مسیر مکانیک آماری" می پردازد. این فصل به قلم ای راجر کراولی و جورج کی هورتون نوشته شده است. و مباحث فرعی همچون " فرمول بندی انتگرال مسیر و تابع تقسیم بندی" ، " روند متغیر و پتانسیل موثر" ، " پتانسیل متغیر درجه دوم" ، " پارامتر گینزبرگ" ، "تقریب جفت شدگی پایین" و بخش های فرعی دیگر را در بر می گیرد. در اینجا متن انگلیسی بخش اول این فصل برای شما دوستان درج می شود و در صورت تمایل به ترجمه می توانید از لینک های دوستان ما که در بخش پیوندهای وبلاگ موجود است اقدام به سفارش ترجمه این فصل کتاب کنید

 

While there exist several formalisms to calculate the lattice dynamical
properties of crystals, no one approach is universally superior. The original
harmonic, or quasi-harmonic, formalism is valid only if the amplitudes of
the atomic vibrations are small. For most materials this restricts the method
to low temperatures. For quantum crystals, the harmonic approximation is
never satisfactory because even the zero-point motion of the atoms is too
large. Anharmonicity can be included through a perturbation expansion and
this extends the temperature range over which the theory can be applied.
However, the successive terms in the perturbation expansion become more
and more complicated, and in some cases the expansion appears to be only
asymptotically convergent. Self-consistent phonon theories were originally
devised to deal with the quantum crystals. The harmonic force constants
are replaced by their averages calculated self-consistently over a trial set of
harmonic oscillator functions. The theory can be shown to be equivalent
to a summation of an infinite subset of the perturbation theory terms. The
great triumph of the first order self-consistent phonon theory (SC1) is that it
provides a physically reasonable starting point for the description of quan-
tum crystals such as helium, but when careful, quantitative, comparisons
are made, the first order theory is usually found to be inadequate. Prob-
ably the best lattice dynamical formalism is the improved self-consistent
theory (ISC), which adds on to the first order theory a non-self-consistent
calculation of the first missing perturbation theory term. It has been found
to give good agreement with experiment in many applications but is clearly
not a complete theory. At some temperature, which is not easily predicted,
the omitted terms must become significant.
This leaves us with the simulation techniques which have been widely
used in recent years. Molecular dynamics and the classical Monte Carlo
method each yield values for a wide range of average quantities which are
in principal exact if quantum mechanical effects are neglected. As more
powerful computers have become widely available, the statistical uncertain-
ties in the averages have been greatly reduced. These theories seem to us to
provide the most satisfactory description of the thermal properties of solids
at high enough temperatures. When quantum effects must be included, at

 

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مقاله مکانیک 5 - فصل اول خصوصیت دینامیک جامدات by: امید ترجمان

فصل اول از کتاب " خصوصیات دینامیک جامدات" به مبحث " تحقیقات مونت کارلو کوانتوم انتگرال مسیر متعلق به خصوصیات ارتعاشی کریستال ها می پردازد. این فصل نوشته آرتور آر مورگان از دپارتمان فیزیکی دانشگاه میشیگان غربی است. این فصل مباحتی همچون " روش های مونت کالرلو کلاسیک: جامدات گاز نجیب" ، " روش های مونت کارلو کوانتومی" ف مونت کارلو کوانتومی وابسته به زمان را دنبال می کند.در این پست بخشی از این مقاله در این کتاب مکانیک جامدات معتبر را می خوانید. برای ترجمه این فصل می توانید از لینک دوستان ما  در بخش پیوندهای وبلاگ استفاده کنید.

In this chapter I will look at some of the recent developments in Monte
Carlo simulations for the static and dynamic thermodynamic properties of
lattice vibrations in quantum mechanical crystaline solids (i.e., the develop-
ment of quantum Monte Carlo methods as they apply to phonons in crys-
tals). This is a relatively new topic in solid state physics even though the
study of the thermodynamics of quantum vibrations in crystaline materials
is one of the first branches of modern physics to be developed (Born and
Huang 1954; Maradudin 1969; Paskiewicz 1987; Xia et al. 1990). The basis
of quantum Monte Carlo simulation techniques as applied to lattice vibra-
tions is the reformulation of the quantum mechanical partition function in
terms of a path integral expressed solely in classical (commuting) variables
(Suzuki 1976a, b, 1987; Suzuki et al. 1977; de Raedt and Lagendijk 1985;
Gubernatis 1986; Negele and Orland 1988; Doll and Gubernatis 1990; Ru-
binstein 1981; Binder 1984, 1986). In the course of this reformulation, one
finds that a d-dimensional quantum partition function is reexpressed as a
(d 1)-dimensional path integral so that the complications of evaluating
a partition function formed of non-commuting operators is carried over to
the evaluation of a higher dimensional classical problem. Our goal in this
chapter will be to present this path-integral reformulation and then to dis-
cuss the evaluation of the thermodynamics of the quantum system in terms
of the evaluation by classical Monte Carlo techniques of averages formed
in the corresponding path-integral formulation. As a final point, contact
will also be made with recent efforts to obtain approximate evaluations of
the path-integral formulation using variational techniques (Feynman 1988;
Samathiyakanit and Glyde 1973; Giachetti and Tognetti 1985-1987; Feyn-
man and Kleinett 1986; Giachetti et al. 1988a, b; Cuccoli et al. 1990,
1992a, b, 1993a; Liu et al. 1991, 1993).

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lمقاله مکانیک 4 - جریان لزج تراکم ناپذیر by: امید ترجمان

این پست مقدمه ای بر جریان لزج تراکم ناپذیر از کتاب " مقدمه ای بر مکانیک سیالات" را بیان می کند و به توزیع سرعت در این قبیل سیالات می پردازد. برای ترجمه مقاله از لینک های دوستان در سایدبار وبلاگ استفاده کنید.

 

In Chapter 3 the effects of pressure in a fluid were isolated (because the fluid was not
moving), and in Chapter 4 the inertia terms were added. The inclusion of viscosity,
its effects, and the resulting velocity distribution are discussed here. For example,
the velocity distribution for the laminar flow inside a pipe is formulated and the
average velocity is calculated. This provides the relation between the simple 1D
average velocity model (of Chapter 4) and the more complex (and realistic) 2D or
3D flows.
The solutions presented early in this chapter are often called exact solutions.
This means that, for a few limited cases, a set of logical assumptions leads to simplifi-
cation of the fluid dynamic equations, which allows their solution (for laminar flow)!
Also, the cases presented in this chapter (e.g., the flow in pipes) is often termed as
internal flows. The discussion on external flows is delayed to the following three
chapters.
The second part of this chapter demonstrates the approach that evolved during
the past 200 years for solving fluid dynamic problems (because there is no closed-
form analytic solution to the complete fluid dynamic equations). According to this
approach, to develop a practical engineering solution, we must start with a simple
but exact solution that determines the major parameters and the basic trends of the
problem (e.g., the pressure drop in a circular pipe versus the Reynolds number).
Based on these parameters, an empirical database can be developed for treating
a wider range of engineering problems. As an example, the viscous laminar flow
model in circular pipes is extended into the high-Reynolds-number range and the
effects of turbulent flow are discussed.


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