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Rouse Model
The Rouse model is one of the simplest coarse-grained descriptions of the dynamics of polymer chains. It treats a single polymer as an Ideal chain of ''N'' point-like beads connected by harmonic springs and neglects both excluded volume and long-range hydrodynamic interactions. Each bead experiences random thermal forces and a Stokes drag, so the chain undergoes overdamped Brownian motion described by Langevin dynamics. Although first proposed for dilute solutions, the model also describes polymer melts whose chain length is below the entanglement threshold. Description A flexible polymer is represented by an ideal freely jointed chain of beads with mean bond length ''l''. Neglecting inertia, the overdamped equation of motion for the position \mathbf_n(t) of bead ''n'' is : \frac=\underbrace_+\underbrace_ where ''k'' is the spring constant, \zeta the one-bead friction coefficient and random force \mathbf f_n(t) a zero-mean Gaussian noise that fulfills the fluctuatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bead Spring Noexclusion
A bead is a small, decorative object that is formed in a variety of shapes and sizes of a material such as stone, bone, shell, glass, plastic, wood, or pearl and with a small hole for threading or stringing. Beads range in size from under 1 mm to over 1 cm in diameter. Beads represent some of the earliest forms of jewellery, with a pair of beads made from ''Nassarius'' sea snail shells dating to approximately years ago thought to be the earliest known example. 2] Beadwork is the art or craft of making things with beads. Beads can be woven together with specialized thread, strung onto thread or soft, flexible wire, or adhered to a surface (e.g. fabric, clay). Etymology The word "bead" derives from Old English ''gebed'', originally meaning "prayer", until transferred to small globular objects. This refers to the use of beads for counting repetitions of prayers, as in Christian Pater Noster cords and rosaries. Types Beads can be divided into several types of overlappin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics ( stress, elasticity, quantum mechanics, fluid mechanics, moment of inertia, ...), electrodynamics ( electromagnetic ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer Physics
Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation of polymers and polymerisation of monomers.P. Flory, ''Principles of Polymer Chemistry'', Cornell University Press, 1953. .Pierre Gilles De Gennes, ''Scaling Concepts in Polymer Physics'' CORNELL UNIVERSITY PRESS Ithaca and London, 1979M. Doi and S. F. Edwards, ''The Theory of Polymer Dynamics'' Oxford University Inc NY, 1986 While it focuses on the perspective of condensed matter physics, polymer physics was originally a branch of statistical physics. Polymer physics and polymer chemistry are also related to the field of polymer science, which is considered to be the applicative part of polymers. Polymers are large molecules and thus are very complicated for solving using a deterministic method. Yet, statistical approaches can yield results and are often pertinent, since large polymers (i.e., polymers with many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reptation
A peculiarity of thermal motion of very long linear macromolecules in ''entangled'' polymer melts or concentrated polymer solutions is reptation. Derived from the word reptile, reptation suggests the movement of entangled polymer chains as being analogous to snakes slithering through one another. Pierre-Gilles de Gennes introduced (and named) the concept of reptation into polymer physics in 1971 to explain the dependence of the mobility of a macromolecule on its length. Reptation is used as a mechanism to explain viscous flow in an amorphous polymer. Sir Sam Edwards and Masao Doi later refined reptation theory. Similar phenomena also occur in proteins. Two closely related concepts are reptons and entanglement. A repton is a mobile point residing in the cells of a lattice, connected by bonds. Entanglement means the topological restriction of molecular motion by other chains. Theory and mechanism Reptation theory describes the effect of polymer chain entanglements on the rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer
A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compound (chemistry), compounds, produces unique physical property, physical properties including toughness, high rubber elasticity, elasticity, viscoelasticity, and a tendency to form Amorphous solid, amorphous and crystallization of polymers, semicrystalline structures rath ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oldroyd-B Model
The Oldroyd-B model is a constitutive model used to describe the flow of viscoelastic fluids. This model can be regarded as an extension of the upper-convected Maxwell model and is equivalent to a fluid filled with elastic bead and spring dumbbells. The model is named after its creator James G. Oldroyd. The model can be written as: \mathbf + \lambda_1 \stackrel = 2\eta_0 (\mathbf + \lambda_2 \stackrel) where: * \mathbf is the deviatoric part of the stress tensor; * \lambda_1 is the relaxation time; * \lambda_2 is the retardation time = \frac\lambda_1 ; * \stackrel is the upper-convected time derivative of stress tensor: \stackrel = \frac \mathbf + \mathbf \cdot \nabla \mathbf -( (\nabla \mathbf)^T \cdot \mathbf + \mathbf \cdot (\nabla \mathbf)) ; *\mathbf is the fluid velocity; *\eta_0 is the total viscosity composed of solvent and polymer components, \eta_0= \eta_s + \eta_p ; *\mathbf is the deformation rate tensor or rate of strain tensor, \mathbf = \frac \left boldsymbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluorescence Correlation Spectroscopy
Fluorescence correlation spectroscopy (FCS) is a statistical analysis, via time correlation, of stationary fluctuations of the fluorescence intensity. Its theoretical underpinning originated from L. Onsager's regression hypothesis. The analysis provides kinetic parameters of the physical processes underlying the fluctuations. One of the interesting applications of this is an analysis of the concentration fluctuations of fluorescent particles (molecules) in solution. In this application, the fluorescence emitted from a very tiny space in solution containing a small number of fluorescent particles (molecules) is observed. The fluorescence intensity is fluctuating due to Brownian motion of the particles. In other words, the number of the particles in the sub-space defined by the optical system is randomly changing around the average number. The analysis gives the average number of fluorescent particles and average diffusion time, when the particle is passing through the space. Eventu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Function
In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined for all complex numbers z except non-positive integers, and for every positive integer z=n, \Gamma(n) = (n-1)!\,.The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: \Gamma(z) = \int_0^\infty t^ e^\textt, \ \qquad \Re(z) > 0\,.The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic function, holomorphic except at zero and the negative integers, where it has simple Zeros and poles, poles. The gamma function has no zeros, so the reciprocal gamma function is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per metre squared, or pascal-seconds. Viscosity quantifies the internal friction, frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls. Experiments show that some stress (physics), stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langevin Equation
In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Langevin equation typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast (microscopic) variables are responsible for the stochastic nature of the Langevin equation. One application is to Brownian motion, which models the fluctuating motion of a small particle in a fluid. Brownian motion as a prototype The original Langevin equation describes Brownian motion, the apparently random movement of a particle in a fluid due to collisions with the molecules of the fluid, m\frac=-\lambda \mathbf+\boldsymbol\left( t\right). Here, \mathbf is the velocity of the particle, \lambda is its damping coefficient, and m is its mass. The force acting on the particle is w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamics (mechanics)
In physics, dynamics or classical dynamics is the study of forces and their effect on motion. It is a branch of classical mechanics, along with ''statics'' and ''kinematics''. The ''fundamental principle of dynamics'' is linked to Newton's second law. Subdivisions Rigid bodies Fluids Applications Classical dynamics finds many applications: * ''Aerodynamics'', the study of the motion of air * '' Brownian dynamics'', the occurrence of Langevin dynamics in the motion of particles in solution * '' File dynamics'', stochastic motion of particles in a channel * ''Flight dynamics'', the science of aircraft and spacecraft design * ''Molecular dynamics'', the study of motion on the molecular level * '' Langevin dynamics'', a mathematical model for stochastic dynamics * '' Orbital dynamics'', the study of the motion of rockets and spacecraft * '' Stellar dynamics'', a description of the collective motion of stars * '' Vehicle dynamics, the study of vehicles in motion Generalizations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruno H
Bruno may refer to: People and fictional characters * Bruno (name), including lists of people and fictional characters with either the given name or surname * Bruno, Duke of Saxony (died 880) * Bruno the Great (925–965), Archbishop of Cologne, Duke of Lotharingia and saint * Bruno (bishop of Verden) (920–976), German Roman Catholic bishop * Pope Gregory V (c. 972–999), born Bruno of Carinthia * Bruno of Querfurt (c. 974–1009), Christian missionary bishop, martyr and saint * Bruno of Augsburg (c. 992–1029), Bishop of Augsburg * Bruno (bishop of Würzburg) (1005–1045), German Roman Catholic bishop * Pope Leo IX (1002–1054), born Bruno of Egisheim-Dagsburg * Bruno II of Brunswick, Bruno II (1024–1057), Frisian count or margrave * Bruno the Saxon (fl. 2nd half of the 11th century), historian * Saint Bruno of Cologne (d. 1101), founder of the Carthusians * Bruno (bishop of Segni) (c. 1045–1123), Italian Roman Catholic bishop and saint * Bruno (archbishop of Trier) (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
