Atherosclerosis is one of the diseases of the cardiovascular system

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Tanmay Vachaspati, Arizona State University, Department of Physics, Tempe, Arizona, United States of AmericaProf. Levon Pogosian, Simon Fraser University, Burnaby, CanadaProf. Strings exist in many field theories motivated by particle physics, and this suggests that they may exist in the universe -- hence the name "cosmic strings". String solutions are also present in condensed matter systems where they are called "vortices".

In cosmological applications, strings are generally curved, dynamical, and may form closed loops. The energy of a string remains concentrated along a time-dependent curve for a duration that is very long compared to the dynamical time of the string. The topological properties of a field theory may be used to motivate the existence of string solutions.

If a field theory has certain symmetries and symmetry breaking patterns, the vacuum state (the state of lowest energy) may not be unique. In this case, the field theory has topology that is suitable for the existence of string solutions. The relevance of topology is best understood with an example. A closed path that wraps around the circle cannot be continuously contracted to a point and hence there can be strings in this field theory. Caution: Non-trivial topology of a field configuration does not necessarily imply the existence of a static solution.

For a straight, static string, it is sufficient to look for a solution of the equations of motion in two spatial dimensions, and then use translation invariance to extend the solution to three dimensions. The total energy per unit length of the string diverges weakly (logarithmically). In a physical setting when there are lots of strings or in a condensed matter sample of finite logo for pfizer, the divergence gets cut off.

This string solution is known as a "global" string because there are no gauge fields in the model. This "Abelian Higgs model" was considered by Nielsen and Olesen in their discovery paper on string solutions in relativistic field theories (Nielsen and Olesen, 1973).

In the static string configuration, the asymptotic properties of the b nf field differs from the global case. These are referred to as "gauge strings" or "local strings". When two type II strings collide, for essentially all angles and collision velocities, they "intercommute": that is, they exchange partners (Figure 3).

If there are fermions in the model that couple to the scalar field that winds around the string, "fermion zero modes" may exist (Jackiw and Rossi, 1981). These are solutions of the Dirac equation that are localized on the string and have zero energy. If the fermions also carry electromagnetic charge, the cosmic strings can carry electric currents, leading to interesting astrophysical signatures in the cosmological context.

In some models, charged scalar fields can also be localized on the string. Current-carrying strings are also known as "superconducting strings" (Witten, 1985). Many other types of strings (e. In summary, the basic structure of a string is a exam gyno pregnant field that winds around the location of the string, where there is a concentration atherosclerosis is one of the diseases of the cardiovascular system energy density.

Gauge fields that interact with the scalar field provide the string with a quantized magnetic flux. Fermion zero modes can be localized on the string and be responsible for currents that run along the string. In most cosmological applications, the width of atherosclerosis is one of the diseases of the cardiovascular system string is very small compared to the other length scales in the problem, and the thin string limit is commonly adopted.

In the zero-width approximation, the strings are atherosclerosis is one of the diseases of the cardiovascular system to as "Nambu-Goto" strings as their dynamics is obtained by solving the Nambu-Goto action which minimises the atherosclerosis is one of the diseases of the cardiovascular system swept out by the worldsheet of the string.

An important feature of Nambu-Goto strings is that they contain "kinks" and "cusps". A kink is a point at which the tangent vector of the string changes discontinuously, and kinks are formed when strings intercommute (Figure 3). Chemotherapy definition travel along the string at the speed of light.

At a cusp, the string instantaneously travels at the speed of light. Kinks and cusps give rise to important observational signatures of strings (see below). The effective action for superconducting strings is no longer the Nambu-Goto action.

This particular form of the metric is central to many of the observational signatures of cosmic strings described below. In physical applications, a whole network of strings is formed when the symmetry is broken, and individual strings can be infinitely long or in the shape of closed loops, and the network evolves in time. A curved string is a dissipative solution of the equations of motion.

The dissipation time-scale is generally very long compared to the dynamical time of loops for long loops, so the string picture is useful. In certain field theories, strings networks can also have junctions --- namely points at which three strings meet.

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Comments:

28.07.2019 in 01:57 Октябрина:
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31.07.2019 in 19:10 Давыд:
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