5,770 research outputs found
On equivalence of equations solutions of gravity field and homogenous inertia field
The metric of a homogenously accelerated system found by Harry Lass is a
solution of the Einstein s equation. The metric of an isotropic homogenous
field must satisfy the new gravitational equation.Comment: 5 pages, 1 figur
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
Molecular Motors Interacting with Their Own Tracks
Dynamics of molecular motors that move along linear lattices and interact
with them via reversible destruction of specific lattice bonds is investigated
theoretically by analyzing exactly solvable discrete-state ``burnt-bridge''
models. Molecular motors are viewed as diffusing particles that can
asymmetrically break or rebuild periodically distributed weak links when
passing over them. Our explicit calculations of dynamic properties show that
coupling the transport of the unbiased molecular motor with the bridge-burning
mechanism leads to a directed motion that lowers fluctuations and produces a
dynamic transition in the limit of low concentration of weak links. Interaction
between the backward biased molecular motor and the bridge-burning mechanism
yields a complex dynamic behavior. For the reversible dissociation the backward
motion of the molecular motor is slowed down. There is a change in the
direction of the molecular motor's motion for some range of parameters. The
molecular motor also experiences non-monotonic fluctuations due to the action
of two opposing mechanisms: the reduced activity after the burned sites and
locking of large fluctuations. Large spatial fluctuations are observed when two
mechanisms are comparable. The properties of the molecular motor are different
for the irreversible burning of bridges where the velocity and fluctuations are
suppressed for some concentration range, and the dynamic transition is also
observed. Dynamics of the system is discussed in terms of the effective driving
forces and transitions between different diffusional regimes
Mechanisms of geometrical seismic attenuation
In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q) observed in many studies according to the effects of geometrical attenuation, which was defined as the zerofrequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling
within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the
physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing) and negative (for focusing). In
media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the
geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within
the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic,
heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These
predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q
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