Gap nodes

From the temperature dependence of the superconducting gap in TmNi2B2C as observed by scanning tunneling spectroscopy (Suderow et al., 2001) a BCS-like superconductivity has been confirmed. A small gap anisotropy was found to be possible but gap nodes were ruled out. A fit using a two-band model agreed well with the spectroscopic data. 

Thus, considering results on y(H) only, a possible unconventional pairing in borocarbides cannot be ruled out. Similarly it has been noted by Dobrosavljevic-Grujic and Miranovic (2003) that a sizable anisotropy of the s-wave gap function leads to strong deviations for the specific heat in the superconducting state from the predictions of the one-band isotropic BCS-Eliashberg theory. In particular, at low temperatures gap-node like dependencies may appear. 

Figure 2.34 illustrates these serious experimental problems. In the upper part (a) the magnetic penetration depth of k-(ET)2Cu(NCS)2 measured by ac susceptibility [220] and in the lower part (b) the same quantity obtained by dc magnetization [227] is shown. The clear discrepancy of the behavior of A(T) at low temperatures is obvious. In the ac-susceptibility experiment consistent with [221, 222, 223] a variation is found. This non-exponential non-BCS dependence can be explained with energy-gap nodes of several different topologies [222]. On the other hand, the data of [227] could very well be described by conventional weak-coupUng theory in the clean limit as shown... 

It may be seen, however, that with the exception of Th, a case to be discussed separately below, all these impurities shift Tq to distinctly lower temperatures and also almost annihilate the expected Cp anomaly. This result is most likely due to inducing immediately a gapless state of superconductivity which would, on that level of impurity concentration, be somewhat surprising for a conventional superconductor but is actually expected for unconventional anisotropic superconducting states where gap nodes on the Fermi surface are easily smeared out. 

Schwann cell A cell that forms the myelin sheath of nerve fibres (axons). Each cell is responsible for a given length of a particular axon (called an Internode) adjacent internodes are separated by small gaps (nodes of Ranvler) where the axon is bare. During its development the cell wraps itself around the fibre, so the sheath consists of concentric layers of Schwann cell membrane. These cells are named after Theodor Schwann. 

Ultrasonic attenuation Sound attenuation has in addition to the propagation direction (q) another polarization (e) degree of freedom and may therefore give even more information on the gap nodes than the thermal conductivity. In HF metals sound attenuation can generally be considered in the hydrodynamic limit where (ox,ql with q, co denoting wave number... 

A more indirect but more versatile method consists in looking for signatures of the gap nodes in the d-density wave states. For low temperatures T A the nodal regions dominate thermodynamics and transport properties. Specific heat and thermal conductivity is equivalent to that of d-SC which have been discussed before. Susceptibility and frequency dependent electrical conductivity however are characteristic for the d-density wave states. Of course there is no vortex phase and the Doppler shift method cannot be applied. 

As usual in the early stage of investigation different experiments gave inconclusive results on the question of the nature of gap anisotropy. The low temperature specific heat exhibits a Cs(T) r" power law in a rather reduced range between 0.65 K and 1.2 K which points to some kind of nodal state. In Sb-NQR experiments (Kotegawa et al., 2003) the nuclear spin lattice relaxation l/Ti rate was determined. It has an itinerant quasiparticle contribution that contains information on the SC nodal state below Tc and in addition a localised contribution from broadened CEF excitations which decreases exponentially for temperatures T A. There is no unique way to separate these contributions, this problem is similar to the two Knight shift contributions in the case of UPd2Al3 (sect. 4.2) with its isoelectronic 5f localised states. The NQR measurements did not show ai r evidence for a coherence peak below Tc which points to an unconventional SC state, for lower temperatures an exponential decay of r, , in conflict with the existence of gap nodes was reported. However, this result depends critically on the subtraction procedure of the localised contribution. 

As the diagram develops, a necessary and sufficient test is applied to pairs of events, and checks for completeness and sequencing are made. One-to-many and many-to-one relations can be represented in the diagram. If data cannot be foimd to verify the relation between an event pair, then a technique called back-STEP can be used to explore gaps in understanding. Essentially back-STEP is a fault tree which uses the event with no other events leading to it as the top node. The analyst then develops possible event flows which could describe what happened during the gap in events in order to cause the top node. 

The nodes of Ranvier are the gaps formed between myelin sheath cells along the axons. The sodium channels are densely localized at the nodes of Ranvier. 

Figure 4.4 Saltatory conduction. Transmission of electrical impulses in a myelinated axon occurs by way of saltatory conduction. Composed primarily of lipid, the myelin sheath insulates the axon and prevents generation of membrane potentials. Membrane potentials occur only at gaps in the myelin sheath, referred to as the nodes of Ranvier. Therefore, transmission of the impulse, or generation of action potentials, occurs only at the nodes.

From the SA node, the heart beat spreads rapidly throughout both atria by way of the gap junctions. As mentioned previously, the atria are stimulated to contract simultaneously. An interatrial conduction pathway extends from the SA node to the left atrium. Its function is to facilitate conduction of the impulse through the left atrium, creating the atrial syncytium (see Figure 13.3). 

An internodal conduction pathway also extends from the SA node and transmits the impulse directly to the atrioventricular (AV) node. This node is located at the base of the right atrium near the interventricular septum, which is the wall of myocardium separating the two ventricles. Because the atria and ventricles are separated from each other by fibrous connective tissue, the electrical impulse cannot spread directly to the ventricles. Instead, the AV node serves as the only pathway through which the impulse can be transmitted to the ventricles. The speed of conduction through the AV node is slowed, resulting in a slight delay (0.1 sec). The cause of this AV nodal delay is partly due to the smaller fibers of the AV node. More importantly, however, fewer gap junctions exist between the cells of the node, which... 

Node of Ranvier The small gap between adjacent segments (internodes) of the myelin sheath. 

It was shown that there were no differences between the flow solutions whether a completely fine mesh was used or a locally refined mesh. This mesh had a node spacing equal to the size of the gap at the sphere contact points at these locations, gradually grading toward a four times coarser node spacing near the voids in the geometry. The node distributions on the sphere surface were also graded from fine near the contact point to coarser away from the... 

These loop-shaped terminations of the sheath at the node are called lateral loops. The loops form membrane complexes with the axolemma called transverse bands, whereas myelin in the internodal region is separated from the axon by an extracellular gap of periaxonal space. The transverse bands are helical structures that seal the myelin to the axolemma but provide, by spaces between them, a tortuous path from the extracellular space to the periaxonal space. 

In general, branch-and-bound [5] is an enumerative search space exploration technique that successively constructs a decision tree. In each node, the feasible region is divided into two or more disjoint subsets which are then assigned to child nodes. During the search space exploration for minimization problems, a lower bound of the objective function is computed in each node and compared against the lowest upper bound found so far. If the lower bound is greater than the upper bound, the corresponding branch is said to be fathomed and not explored anymore. The exploration terminates when a certain gap between the upper and the lower bound is reached or when the all possible subsets have been enumerated. 

As a characteristic feature, both the gap functions have nodes at poles (9 = 0,7r) and take the maximal values at the vicinity of equator (9 = 7t/2), keeping the relation, A > A+. This feature is very similar to 3P pairing in liquid 3He or nuclear matter [17, 18] actually we can see our pairing function Eq. (39) to exhibit an effective P wave nature by a genuine relativistic effect by the Dirac spinors. Accordingly the quasi-particle distribution is diffused (see Fig. 3)... 

Oligodendrocytes are present in the CNS as well and wrap around axons to form a myelin sheath. Myelin wraps into concentric layers that spiral around the axon. Gaps in the oligodendrocytes are the nodes of Ranvier, where the membrane maintains contact with extracellular fluid. The nodes serve to propagate the action potential in myelinated axons. Schwann cells perform an analogous function, myelinating axons in the peripheral nervous system. Not all neurons are myelinated, but myelination increases the metabolic efficiency of action potentials. Demyelination of neurons produces deficits in neuronal conduction, as is seen in multiple sclerosis. 

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