Curie principle

Once again, these fluxes are not all independent and some care must be taken to rewrite everything so that syimnetry is preserved [12]. Wlien this is done, the Curie principle decouples the vectorial forces from the scalar fluxes and vice versa [9]. Nevertheless, the reaction temis lead to additional reciprocal relations because... 

The lack of correlation between the flucUiating stress tensor and the flucUiating heat flux in the third expression is an example of the Curie principle for the fluctuations. These equations for flucUiating hydrodynamics are arrived at by a procedure very similar to that exliibited in the preceding section for difllisioii. A crucial ingredient is the equation for entropy production in a fluid... 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

The rate of a chemical reaction (the chemical flux ), 7ch, in contrast to the above processes, is a scalar quantity and, according to the Curie principle, cannot be coupled with vector fluxes corresponding to transport phenomena, provided that the chemical reaction occurs in an isotropic medium. Otherwise (see Chapter 6, page 450), chemical flux can be treated in the same way as the other fluxes. 

The rate of the active transport of sodium ion across frog skin depends both on the electrochemical potential difference between the two sides of this complex membrane (or, more exactly, membrane system) and also on the affinity of the chemical reaction occurring in the membrane. This combination of material flux, a vector, and chemical flux (see Eq. 2.3.26), which is scalar in nature, is possible according to the Curie principle only when the medium in which the chemical reaction occurs is not homogeneous but anisotropic (i.e. has an oriented structure in the direction perpendicular to the surface of the membrane or, as is sometimes stated, has a vectorial character). 

When the incident light is vertically polarized, the vertical axis Oz is an axis of symmetry for the emission of fluorescence according to the Curie principle, i.e. Ix = Iy. The fluorescence observed in the direction of this axis is thus unpolarized. 

I may be wrong, but I seem to remember that according to the Curie principle, there can be no direct coupling between a vectorial flux and a scalar chemical reaction. That would mean that there is no coupling coefficient L+r, which is essential for the calculation of the efficiency. I wonder what conditions have to be fulfilled for this coupling between a chemical reaction and the vectorial flux to occur. 

This specter should once and for all be laid to rest. The Curie principle as it applies to the system at hand (I will not state it in its most general form) forbids, in the linear regime, coupling between a vectorial process such as a flow and a scalar process such as a chemical reaction in an isotropic space. However, active transport does not occur in an isotropic or symmetrical system. Clearly, the protein constituting the pump is uniquely oriented within the membrane. 

The capabilities of MEIS and the models of kinetics and nonequilibrium thermodynamics were compared based on the theoretical analysis and concrete examples. The main MEIS advantage was shown to consist in simplicity of initial assumptions on the equilibrium of modeled processes, their possible description by using the autonomous differential equations and the monotonicity of characteristic thermodynamic functions. Simplicity of the assumptions and universality of the applied principles of equilibrium and extremality lead to the lack of need in special formalized descriptions that automatically satisfy the Gibbs phase rule, the Prigogine theorem, the Curie principle, and some other factors comparative simplicity of the applied mathematical apparatus (differential equations are replaced by algebraic and transcendent ones) and easiness of initial information preparation possibility of sufficiently complete consideration of specific features of the modeled phenomena. 

It is important in an isotropic medium that the reciprocity coefficients Ly are nonzero only when the interacting thermodynamic forces Xj have the same spatial dimensions (for example, they are both scalars, vectors, or tensors). This is the so called Curie principle. In nonisotropic systems— for example, at the interaction of processes on functional membranes— the Curie principle may be inoperable. 

Notice that, formally, the possibility of this conjunction violates the Curie principle, which forbids the conjunction of a scalar process (synthe sis of a substance) and a vectorial process (the proton transport through the membrane). Nevertheless, this contradiction is avoided due to the pres ence of a special conjugation tool like an anisotropic membrane. 

From the Curie principle and symmetry considerations it can be shown that for an isotropic medium, the first and second moments Ff° (t) and F g are generally sufficient for a complete description of the system The interactions used in spectroscopic experiments as ESR, NMR and FAD are affected only by the second moment of the OACF ... 

A general statement of this argument is that in an isotropic system flows and forces of different tensorial orders are not coupled. This is known as the Curie principle. Systems that are anisotropic often have some elements of symmetry which reduce the number of nonzero coefficients from the maximum of n2. To prove these relations one must apply the arguments of Chapter 11 involving parity, reflection symmetries, rotational symmetries, and time-reversal symmetries. 

The opposition living-inert fakes a very important place in Vernadsky s concept. Every significant theoretical statement of Iris theory is cormected with this juxtaposition (1) the Pasteur-Curie principle, (2) the Redi principle, (3) the dissymmetry concept, (4) the three biogeochemical princ ies and (5) the statement about the impossibihty of abiogenesis. 

We also note that the vector or tensor responses (3.187), (3.189) depend only on the vector or tensor driving forces respectively. This fact is known in linear irreversible thermodynamics as the Curie principle [36, 80, 88, 89] (cf. discussion in [34, 38]). Present theory shows however, that this property follows from the isotropy of constitutive functions and from the representation theorems of such linear functions, see Appendix A.2, Eqs.(A.ll)-(A.13) and (A.57)-(A.59). But representation theorems for nonlinear isotropic constitutive functions [64, 65] show that the Curie principle is not valid generally. 

Of course this important reduction (known also as the Curie principle roughly asserting that response of given tensor rank (scalar, vector and tensor) depends on variables of the same tensor rank [2-4, 119, 120]) is valid only in this linear case [12, 13]. The non-linear case is much more complicated [79, 121-123]. 

The emergence of the homochiral proteins and nucleic acids, composed from residues of I-amino acids and D-sugars respectively, from the achiral prebiotic world still provides an unsolved conundrum in the field of the origin of life. This mist results from the fundamental symmetry rules as defined, at the end of the nineteenth century, by the Curie principle [1], which states that, . .. a physical event cannot have a symmetry lower than that of the event that caused it ... 

Kedem ° attempted to circumvent the paradox implicit in the driving of vectorial transport processes with supposedly scalar chemical forces by introducing a vectorial cross coefficient in a non-equilibrium thermodynamic definition of active transport. Jardetzky , however, stated that the direct coupling between a metabolic reaction and a transport process, implied by Kedem s vectorial cross coefficient, was impossible because it would contravene the Curie principle (see also ref. 11). Katchalsky and Kedem, later supported by Moszynski et al, answered the criticism of Jardetzky by saying that Langeland had shown that the principle of Curie applies... 

This kind of information exists, and, moreover, is included in a general principle at the groups theory level, but which fully manifests its applicability in crystallographic analysis it is called as (Pierre) Curie Principle... 

FIGURE 2.57 Application of Curie Principle for the point group 42m during the action of an external field, with the representative vector polarized in various directions after (Hartmann, 2003, Conunission on Ciystallographic Teaching lUCR 2013). 

Yet, the application of the Curie principle has another practical importance due to the lowering of the crystal symmetry under the external influence, the anisotropy is practically increased, such that the initially uniaxial crystals becomes biaxial, thus increasing its optical activity. 

Yet, even by appealing to other phenomena and interactions (e g., the X-ray diffraction on crystals), the Curie Principle, by its various equivalent formulations, allows the individualization of the symmetry effect in Nature s phenomena and classification. 

Interpreting the Friedel effect/law of inducing of an inversion center in a crystal (unit cell) structure by optical perturbation, in special due to the X-ray near-edge of absorption of characteristic spectra Connecting the physical perturbation of crystal S5mimetry with Curie principle that provides a practical receipt characterizing the system + perturbation common symmetry by considering their commonalities ... 

Once the spatial group determined, from the structure determination, this structure can be further characterized following all the correlated properties with the existing symmetry elements and operations (in accordance with the so-called Neumann s principle, se also the Curie Principle of Section 2.5.8.2). Consequently, there is again emphasized the importance of the accuracy with which the structure is determined or the method is refined. 

The first two forces are vectors, while the last is a scalar, so they do not couple (The Curie principle). Possible choices for the frame of reference are the centre of mass, the average volume, the average molar and the solvent velocity. In heterogeneous systems, the natural frame of reference is the surface. ... 

With the application of the Curie principle from this general result we have the reciprocal relations for isotropic case, [1], [2], [25], Due to the Curie-piinciple the... 

In a shorter reformulation this means that the effects may occasionally have the same or a higher symmetry than the causes, but the latter cannot have a higher symmetry than the effects produced [16], possible violations of the Curie principle in some nonlinear phenomena (see, e.g.. Ref. 17) may be ignored here. Curie also stated that asymmetry is essential to characterize physical phenomena What is necessary is that certain symmetry elements are missing Asymmetry is what creates the phenomenon ([15], p. 400). 

The Curie principle is a symmetry rule by which one can relate things of one tensorial type to another [5>6]. For example... 

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