Thermal fluctuation

Johnson noise and thermal fluctuations are briefly discussed below, Johnson noise because it is usually the dominant noise and thermal fluctuations because they set a lower limit on the achievable noise level. 

Johnson noise arises because the random thermal motion of electrons in an isolated resistor produces random fluctuations in voltage between its ends, covering a broad frequency band. It can be shown that 

The root mean square (r.m.s.) noise voltage AFj for unit bandwidth is A/j/ Y, where A/j is the r.m.s. noise current for unit bandwidth and Y is the admittance. Therefore 

Under the conditions defined the material parameter to be maximized is p, with c, e and tan 3 minimized as required by Fd (Eq. (7.22)). 

Thermal fluctuations arise even when a body is in thermal equilibrium with its surroundings through radiation exchange only. Calculation of the mean-square 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially 

This static alloy analogy picture should be a good description as long as there is a separation of timescales. If this breaks down, dynamical fluctuations—or quantum fluctuations— which are beyond this static picture, become important. These quantum fluctuations are the main emphasis of DMFT (Georges et al., 1996), which maps the system onto an effective Anderson impurity model, describing a dynamically fluctuating impurity in a self-consistently determined effective host. So far, DMFT has been formulated for model Hamiltonians, such as the Hubbard model, and material-specific results have been achieved by constructing these model Hamiltonians from realistic band structure calculations. In 

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The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Peskin C S, Odell G M and Oster G F 1993 Cellular motions and thermal fluctuations the Brownian ratchet Biophys. J. 65 316... 

A3.3.2 EQUILIBRIUM SYSTEMS THERMAL FLUCTUATIONS AND SPATIO-TEMPORAL CORRELATIONS... 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

In other cases, the inherent flaws or perturbations responsible for fracture are less easily recognized. The internal spalling of glass or the cavitation of a rapidly expanding liquid are examples although even here, some form of imperfection such as impurities, dislocations, or thermal fluctuations are expected to play an important role in nucleating the fracture process. 

J. L. Harden, D. Andelman. Thermal fluctuations of thin wetting films on disordered solids. Langmuir 5 2547-2551, 1992. 

Of the variety of quantum effects which are present at low temperatures we focus here mainly on delocalization effects due to the position-momentum uncertainty principle. Compared to purely classical systems, the quantum delocalization introduces fluctuations in addition to the thermal fluctuations. This may result in a decrease of phase transition temperatures as compared to a purely classical system under otherwise unchanged conditions. The ground state order may decrease as well. From the experimental point of view it is rather difficult to extract the amount of quantumness of the system. The delocahzation can become so pronounced that certain phases are stable in contrast to the case in classical systems. We analyze these effects in Sec. V, in particular the phase transitions in adsorbed N2, H2 and D2 layers. 

To define the correlation functions of partly quenched systems requires one to consider fluctuations. There are two types of fluctuations thermal fluctuations for a given configuration of matrix species, and fluctuations induced by disorder. We characterize the average over disorder of thermal fluctuations by the variance... 

In particular we would like to treat some essential effects of fluctuations where we assume that, for example, thermal fluctuations exist and are localized in space and time. The effects on large lengths and long times are then of interest where the results are independent of local details of the model assumptions and therefore will have some universal validity. In particular, the development of a rough surface during growth from an initially smooth surface, the so-called effect of kinetic roughening, can be understood on these scales [42,44]. 

To examine replication of IPBs we made MFKEi-based simulations using the simplest 2D alloy model with the nearest-neighbor interaction. Some results are presented in Figs. 8-10. The lower row in Fig. 10 illustrates possible effects of thermal fluctuations, similar to those discussed in Sec. 3 for the replication of APBs. The figure shows that peculiar features of microstructural evolution are preserved even under rather strong thermal fluctuations used in this simulation. 

An ordering phase transition is characterized by a loss of symmetry the ordered phase has less symmetry than the disordered one. Hence, an ordering process leads to the coexistence of different domains of the same ordered phase. An interface forms whenever two such domains contact. The thermodynamic behavior of this interface is governed by different forces. The presence of the underlying lattice and the stability of the ordered domains tend to localize the interface and to reduce its width. On the other hand, thermal fluctuations favor an interfacial wandering and an increase of the interface width. The result of this competition depends strongly on the order of the bulk phase transition. 

Consider a physical system with a set of states a, each of which has an energy Hio). If the system is at some finite temperature T, random thermal fluctuations will cause a and therefore H a) to vary. While a system might initially be driven towards one direction (decreasing H, for example) during some transient period immediately following its preparation, as time increases, it eventually fluctuates around a constant average value. When a system has reached this state, it is said to be in thermal equilibrium. A fundamental principle from thermodynamics states that when a system is in thermal equilibrium, each of its states a occurs with a probability equal to the Boltzman distribution P(a) ... 

Leadbetter AJ, Norris EK (1979) Molec Phys 38 669. There are different contributions which give rise to a broadening a of the molecular centre of mass distribution function f(z). The most important are the long-wave layer displacement thermal fluctuations and the individual motions of molecules having a random diffusive nature. The layer displacement amplitude depends on the magnitude of the elastic constants of smectics ... 

Since Ca is transferred from one side of the membrane to the other side in association with the Ca -ATPase, thermal fluctuation of critical regions of the Ca -ATPase influenced in specific ways through the phosphorylation of the enzyme by ATP may play a role in Ca translocation. Similar ideas have been proposed some time ago by Huxley [419] in relationship to crossbridge movements during muscle contraction and by Welch and others on the role of protein fluctuations in enzyme action [420-430]. 

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