The penetration of microwaves in various materials gives active microwave imaging a large potential for subsurface radar, civil engineering etc. Several inverse-scattering theories have been proposed in the scientific literature. Among them, the simplest Bom-type approach, which does not take into account multiple reflections, is valid for weakly scattering objects [1-2]. To improve the quality of reconstruction, the method based on the successive application of the perturbative algorithm was developed [3]. However, the inherent approximations of this approach are not overcome in the iterative scheme. Another class of algorithms aims to obtain the spatial distribution of permittivity by using numerical solutions of exact equations [4-6]. Unfortunately, a rate of convergence of the solution to the global minimum of cost function depends on actual contrast values, measurement error etc. That is why an importance of a priori knowledge about the object imder investigation is usually emphasized. In general, existing inversion algorithms suffer from serious problems when discontinuous profiles of high contrast, which are often encountered in practical applications, are to be reconstructed. Moreover, the frequency-swept imaging methods utilize usually reflection coefficient data measured in a very broad frequency band starting from zero frequency [1-2, 4-5]. Such methods are inappropriate from an application point of view.  [c.127]

T.M. Habashy, W.C. Chew, and E.Y. Chow, Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab, Radio Sci., 1986,21,  [c.130]

W.C. Chew and Y.M. Wang. Reconstruction of two-dimensional permittivity distribution using the distorted born iterative method. IEEE Transaetions on Medical Imaging, 9, 1990.  [c.333]

The whole structure is rigid but open, giving ice a low density. The structure of liquid water is similar but less rigid this explains the fact that water has a high melting point and dielectric constant (permittivity). Hydrogen bonding has been suggested as one reason why both H and OH ions have very high ionic mobilities.  [c.53]

Because of the presence of the lone pairs of electrons, the molecule has a dipole moment (and the liquid a high permittivity or dielectric constant).  [c.269]

The high permittivity (dielectric constant) makes water a highly effective solvent for ionic crystals, since the electrostatic attractive forces between oppositely charged ions are reduced when the crystal is placed in water. Moreover, since water is not composed of randomly arranged molecules but has some degree of structure , the introduction of charged ions which attract the polar water molecules, produces a new structure , and a fraction of the water molecules become associated with the ions—the process known as hydration. Energy is evolved in this process—hydration energy—and this assists the solution of both ionic and partly covalent substances in the latter case hydrolysis may also occur (see below). There are, however, many non-ionic substances for which water is a good solvent this is because the molecules of such substances almost always contain hydrogen and oxygen atoms which can form hydrogen bonds with water molecules. Hence, for example, substances containing the —OH group, for example alcohols, carboxylic acids and some carbohydrates, are soluble in water, provided that the rest of the molecule is not too large.  [c.270]

The dipole moments of the hydrogen halides decrease with increasing atomic number of the hydrogen, the largest difference occurring between HF and HCl, and association of molecules is not an important factor in the properties of FICl, HBr and HI. This change in dipole moment is reflected in the diminishing permittivity (dielectric constant) values from HF to HI.  [c.327]

The liquid, like water, has a high dielectric constant (permittivity) and is weakly conducting. It is a good solvent for many inorganic and organic substances, to give conducting solutions. Substances which move the equilibria to the right when dissolved in hydrogen fluoride, by taking up the fluoride ions, are acids . For example, boron trifluoride forms the tetrafluoroborate anion in a solution of hydrogen fluoride  [c.329]

The basic assumption underlying the method described here for predicting ionization equilibria in proteins is that each AAG° is electrostatic in origin. Within the framework of the PB model for the solute-solvent system, AAG° can be computed from the 4 electrostatic free energies based on the following sets of point charges representing the residue in its isolated state and as a titratable group in the protein a) a set of charges representing the neutral form of the residue and b) a set of charges representing the charged form of the residue. The energy necessary to assemble the whole set of n point charges in an arbitrary dielectric body of ei immersed in an infinite medium with another dielectric constant eg (provided there is no field dependence of the permittivity of the dielectric) is [4]  [c.179]

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section  [c.345]

Within Eqs. (38) and (39), q, and Oj are the charge and the radius of the ith of N particles, respectively. The dielectric permittivity of the system is described by e.  [c.364]

Fi. 4.30 A sigmoidal dielectric model smoothly varies the effective permittivity from SO to 1 as shown.  [c.221]

Li) he so-called distance-dependent dielectric models. The simplest implementation of a dis-i.iiice-dependent dielectric is to make the relative permittivity proportional to the distance. Tine interaction energy between two charges qi and qj then becomes  [c.221]

A line joining two points may pass through regions of different permittivity.  [c.222]

A fourth correction term may also be required, depending upon the medium that surrounds the sphere of simulation boxes. If the surrounding medium has an infinite relative permittivity (e.g. if it is a conductor) then no correction term is required. However, if the surrounding medium is a vacuum (with a relative permittivity of 1) then the following energy must be added  [c.351]

It is necessary to use the bulk permittivity of the solvent in the equation, instead of the unknown but more correct effective permittivity of the medium between the charges in the transition state.  [c.155]

Even the bulk permittivities of aqueous sulphuric acid solutions are unknown.  [c.155]

Also use constant dielectric for MM+ and OPLS calculations. Use the distance-dependent dielectric for AMBER and BlO-t to mimic the screening effects of solvation when no explicit solvent molecules are present. The scale factor for the dielectric permittivity, 8, can vary from 1 to 80. HyperChem sets 8 to 1.5 for MM-t. Use 1.0 for AMBER and OPLS, and 1.0-2.5 for BlO-t.  [c.104]

The first modification is to simply scale the dielectric permittivity of free space (8 ) by a scale factor D to mediate or dampen the long range electrostatic interactions. Its value was often set to be between 1.0 and 78.0, the macroscopic value for water. A value of D=2.5, so that 8 =2.58q, was often used in early CHARMM calculations.  [c.180]

T.J. Cui and C.H. Liang, Reconstruction of the permittivity profile of an inhomogeneous medium using an equivalent network method, 1993, IEEE Trans. Antennas Propagat., 41, pp. 1719-1726.  [c.130]

One of the reasons why water is such an outstanding solvent is its high dielectric constant, which effectively reduces charge-charge interactions by electrostatic shielding. To account for this effect in a relatively simple manner, the first modification introduced into the Coulomb term, which describes electrostatic interactions, was a re-scaling of the dielectric permittivity of free space Sq by a factor D, This damps the long-range electrostatic interactions according to the relationship E = Deq. Using the macroscopic value for water (D = 78.0), e then amounts to 78.0 0- An alternative way is to introduce a distance dependence into the electrostatic interactions by defining an effective dielectric constant s = DeQrij, which modifies to the Coulomb term of Eq. (32) according to Eq. (37).  [c.364]

I be value of gff varies from a value of 1 at zero separation to Sy (the bulk permittivity of the soK ent) at large distances, in a maimer determined by the parameter S (which is typically gi ea a value between 0.15 and 0.3 A Figure 4.30). Sigmoidal functions give better behaviour than the simple distance-dependent dielectric model. However, it may be difficult to choose the appropriate value for the bulk dielectric , when performing calculations on large solutes, as the shortest distance between two charges may be through the solute mulecule rather than through the solvent (Figure 4.31).  [c.221]

In this formula, which is presented here in the rationalised s.i. form, e is the permittivity of the medium (the product of the dielectric constant and the permittivity of a vacuum) and r is the distance of separation of the charges in the transition state. For two monocations with r = 0-2 run in water at 25 °C (for which medium e = 7-0 x kg m" s and (Slne/Sr) = — 0-0046 K ), AS i === — 4oJK mol . This then is the magnitude of the difference in entropies of activation to be expected for the elementary reaction in water at 25 °C between the nitronium ion and a neutral molecule on the one hand, and the nitronium ion and a cation on the other. This is equivalent to the expectation that the term logio( /l mol s ), where A is the Arrhenius pre-exponential factor, would be greater by about 2 for reactions of neutral molecules than for reactions of cationic substrates with the nitronium ion. However, there are (at least) five serious drawbacks to the use of this expectation as a criterion to decide whether a positively charged conjugate acid or a neutral free base is the species imdergoing nitration. These are  [c.155]

See pages that mention the term Permittivity : [c.128]    [c.32]    [c.170]    [c.216]    [c.231]    [c.233]    [c.502]    [c.502]    [c.503]    [c.104]    [c.178]    [c.180]    [c.220]    [c.221]    [c.257]    [c.416]    [c.614]    [c.124]    [c.179]    [c.179]    [c.178]    [c.79]    [c.85]   
Modelling molecular structures (2000) -- [ c.13 ]