124,447 research outputs found
Quaternion Electromagnetism and the Relation with 2-Spinor Formalism
By using complex quaternion, which is the system of quaternion representation
extended to complex numbers, we show that the laws of electromagnetism can be
expressed much more simply and concisely. We also derive the quaternion
representation of rotations and boosts from the spinor representation of
Lorentz group. It is suggested that the imaginary 'i' should be attached to the
spatial coordinates, and observe that the complex conjugate of quaternion
representation is exactly equal to parity inversion of all physical quantities
in the quaternion. We also show that using quaternion is directly linked to the
two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and
sedenion in physics as n-fold rotationComment: Version published in journal Universe (2019
Robustness of the avalanche dynamics in data packet transport on scale-free networks
We study the avalanche dynamics in the data packet transport on scale-free
networks through a simple model. In the model, each vertex is assigned a
capacity proportional to the load with a proportionality constant . When
the system is perturbed by a single vertex removal, the load of each vertex is
redistributed, followed by subsequent failures of overloaded vertices. The
avalanche size depends on the parameter as well as which vertex triggers
it. We find that there exists a critical value at which the avalanche
size distribution follows a power law. The critical exponent associated with it
appears to be robust as long as the degree exponent is between 2 and 3, and is
close in value to that of the distribution of the diameter changes by single
vertex removal.Comment: 5 pages, 7 figures, final version published in PR
Evolution of the Protein Interaction Network of Budding Yeast: Role of the Protein Family Compatibility Constraint
Understanding of how protein interaction networks (PIN) of living organisms
have evolved or are organized can be the first stepping stone in unveiling how
life works on a fundamental ground. Here we introduce a hybrid network model
composed of the yeast PIN and the protein family interaction network. The
essential ingredient of the model includes the protein family identity and its
robustness under evolution, as well as the three previously proposed ones: gene
duplication, divergence, and mutation. We investigate diverse structural
properties of our model with parameter values relevant to yeast, finding that
the model successfully reproduces the empirical data.Comment: 5 pages, 5 figures, 1 table. Title changed. Final version published
in JKP
Inclusive angular distribution of alpha and Li fragments produced in the Fe-C and Fe-Pb collisions at 1.88 GeV/u
The LS (laboratory system) emission angles theta for 2188 and 298 Li fragments, produced inclusively in relativistic Fe-C and Fe-Pb collisions, have been measured in reference to incident Fe-ion beam tracks nearby in nuclear emulsion. An empirical differential frequency formula, dN(cot theta) = exp (a + b cot theta)d(cot theta) is obtained with the constant b approx. = -0.026 at 1.88 GeV/u, which seems to be independent on the kinds of target nucleus as well as on the kinds of projectile fragments
Quantum network architecture of tight-binding models with substitution sequences
We study a two-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. Substitution sequences are known to underlie aperiodic
structures. We show that parameter inputs \alpha_m described by such sequences
can lead here to a quantum dynamics, intermediate between the regular and the
chaotic variant. Exponential parameter sensitivity characterizing chaotic
quantum Turing machines turns out to be an adequate criterion for induced
quantum chaos in a quantum network.Comment: Accepted for publication in J. mod. Optics [Proc. Workshop
"Entanglement and Decoherence", Gargnano (Italy), Sept 1999], 3 figure
Betweenness centrality correlation in social networks
Scale-free (SF) networks exhibiting a power-law degree distribution can be
grouped into the assortative, dissortative and neutral networks according to
the behavior of the degree-degree correlation coefficient. Here we investigate
the betweenness centrality (BC) correlation for each type of SF networks. While
the BC-BC correlation coefficients behave similarly to the degree-degree
correlation coefficients for the dissortative and neutral networks, the BC
correlation is nontrivial for the assortative ones found mainly in social
networks. The mean BC of neighbors of a vertex with BC is almost
independent of , implying that each person is surrounded by almost the
same influential environments of people no matter how influential the person
is.Comment: 4 pages, 4 figures, 1 tabl
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