Complex conjugate time in macro-experiments

2002 ◽  
Vol 13 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Jakub Czajko
Keyword(s):  
Complex Conjugate ◽  
Conjugate Time

scholarly journals Time-Domain Studies of General Dispersive Anisotropic Media by the Complex-Conjugate Pole–Residue Pairs Model

2021 ◽  
Vol 11 (9) ◽  
pp. 3844
Author(s):  
Konstantinos P. Prokopidis ◽  
Dimitrios C. Zografopoulos
Keyword(s):  
Time Domain ◽  
Electromagnetic Wave Propagation ◽  
Frequency Dispersion ◽  
Magnetized Plasma ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Pole Residue ◽  
Permittivity And Permeability ◽  
Arbitrary Frequency ◽  
Difference Time

A novel finite-difference time-domain formulation for the modeling of general anisotropic dispersive media is introduced in this work. The method accounts for fully anisotropic electric or magnetic materials with all elements of the permittivity and permeability tensors being non-zero. In addition, each element shows an arbitrary frequency dispersion described by the complex-conjugate pole–residue pairs model. The efficiency of the technique is demonstrated in benchmark numerical examples involving electromagnetic wave propagation through magnetized plasma, nematic liquid crystals and ferrites.

COMPLEX MASS FERMIONIC FIELDS

1994 ◽  
Vol 09 (12) ◽  
pp. 2103-2115 ◽  
Author(s):  
D.G. BARCI ◽  
L.E. OXMAN
Keyword(s):  
Degrees Of Freedom ◽  
Order Equation ◽  
Complex Conjugate ◽  
Zero Energy ◽  
Natural Representation ◽  
Symmetric State ◽  
Fermionic Field ◽  
Fermionic Fields ◽  
Real Mass ◽  
Mass Case

We consider a fermionic field obeying a second order equation containing a pair of complex conjugate mass parameters. After obtaining a natural representation for the different degrees of freedom, we are able to construct a unique vacuum as the more symmetric state (zero energy-momentum, charge and spin). This representation, unlike the real mass case, is not holomorphic in the Grassmann variables. The vacuum eigenstate allows the calculation of the field propagator which turns out to be half advanced plus half retarded.

scholarly journals Consecutive ruptures on a complex conjugate fault system during the 2018 Gulf of Alaska earthquake

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shinji Yamashita ◽  
Yuji Yagi ◽  
Ryo Okuwaki ◽  
Kousuke Shimizu ◽  
Ryoichiro Agata ◽  
...  
Keyword(s):  
Gulf Of Alaska ◽  
Source Model ◽  
Fault System ◽  
Complex Conjugate ◽  
Inversion Method ◽  
Fault Geometry ◽  
Conjugate System ◽  
Finite Fault Inversion ◽  
Finite Fault ◽  
Alaska Earthquake

AbstractWe developed a flexible finite-fault inversion method for teleseismic P waveforms to obtain a detailed rupture process of a complex multiple-fault earthquake. We estimate the distribution of potency-rate density tensors on an assumed model plane to clarify rupture evolution processes, including variations of fault geometry. We applied our method to the 23 January 2018 Gulf of Alaska earthquake by representing slip on a projected horizontal model plane at a depth of 33.6 km to fit the distribution of aftershocks occurring within one week of the mainshock. The obtained source model, which successfully explained the complex teleseismic P waveforms, shows that the 2018 earthquake ruptured a conjugate system of N-S and E-W faults. The spatiotemporal rupture evolution indicates irregular rupture behavior involving a multiple-shock sequence, which is likely associated with discontinuities in the fault geometry that originated from E-W sea-floor fracture zones and N-S plate-bending faults.

scholarly journals Clebsch–Gordan coefficients of discrete groups in subgroup bases

2018 ◽  
Vol 33 (10) ◽  
pp. 1850055
Author(s):  
Gaoli Chen
Keyword(s):  
Discrete Group ◽  
Irreducible Representations ◽  
Complex Conjugate ◽  
Discrete Groups

We express each Clebsch–Gordan (CG) coefficient of a discrete group as a product of a CG coefficient of its subgroup and a factor, which we call an embedding factor. With an appropriate definition, such factors are fixed up to phase ambiguities. Particularly, they are invariant under basis transformations of irreducible representations of both the group and its subgroup. We then impose on the embedding factors constraints, which relate them to their counterparts under complex conjugate and therefore restrict the phases of embedding factors. In some cases, the phase ambiguities are reduced to sign ambiguities. We describe the procedure of obtaining embedding factors and then calculate CG coefficients of the group [Formula: see text] in terms of embedding factors of its subgroups [Formula: see text] and [Formula: see text].

Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown

1999 ◽  
Vol 396 ◽  
pp. 73-108 ◽  
Author(s):  
D. M. MASON ◽  
R. R. KERSWELL
Keyword(s):  
Finite Amplitude ◽  
Complex Conjugate ◽  
Small Scale ◽  
Conjugate Pair ◽  
Weakly Nonlinear ◽  
Elliptical Instability ◽  
Elliptical Flow ◽  
Complex Conjugate Pair ◽  
Generic Instability ◽  
Secondary Instabilities

A direct numerical simulation is presented of an elliptical instability observed in the laboratory within an elliptically distorted, rapidly rotating, fluid-filled cylinder (Malkus 1989). Generically, the instability manifests itself as the pairwise resonance of two different inertial modes with the underlying elliptical flow. We study in detail the simplest ‘subharmonic’ form of the instability where the waves are a complex conjugate pair and which at weakly supercritical elliptical distortion should ultimately saturate at some finite amplitude (Waleffe 1989; Kerswell 1992). Such states have yet to be experimentally identified since the flow invariably breaks down to small-scale disorder. Evidence is presented here to support the argument that such weakly nonlinear states are never seen because they are either unstable to secondary instabilities at observable amplitudes or neighbouring competitor elliptical instabilities grow to ultimately disrupt them. The former scenario confirms earlier work (Kerswell 1999) which highlights the generic instability of inertial waves even at very small amplitudes. The latter represents a first numerical demonstration of two competing elliptical instabilities co-existing in a bounded system.

Vibrations of Spinning Rings With Radial and Circumferential Displacement Constraints

1991 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Chen-Kai Su
Keyword(s):  
Natural Frequencies ◽  
Point Contact ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Complex Conjugate ◽  
Constrained System ◽  
Form Complex ◽  
Circumferential Displacement ◽  
On The Road ◽  
Displacement Constraints

Abstract The frequencies and mode shapes of rolling rings with radial and circumferential displacement constraints are investigated. The displacement constraints practically come from the point contact, e.g., rolling tire on the road, or other applications. The proposed approach to analysis is calculating the natural frequencies and modes of a non-contacted spinning ring, then employing the receptance method for displacement constraints. The frequency equation for the constrained system is hence obtained, and it can be solved numerically or graphically. The receptance matrix developed for the spinning ring is surprisingly found not symmetric as usual. Moreover, the cross receptances are discovered to form complex conjugate pairs. That is a feature that has never been described in literature. The results show that the natural frequencies for the spinning ring in contact, as expected, higher than those for the non-contacted ring. The variance of frequencies to rotational speeds are then illustrated. The analytic forms of mode shapes are also derived and sketched. The traveling modes are then shown for cases.

The 2019 Ms 4.2 and 5.2 Beiliu Earthquake Sequence in South China: Complex Conjugate Strike-Slip Faulting Revealed by Rupture Directivity Analysis

2021 ◽  
Author(s):  
Xiaohui He ◽  
Hao Liang ◽  
Peizhen Zhang ◽  
Yue Wang
Keyword(s):  
South China ◽  
Source Parameters ◽  
Active Faults ◽  
Fault Zones ◽  
Strike Slip ◽  
P Wave ◽  
Complex Conjugate ◽  
South China Block ◽  
Rupture Directivity ◽  
Time Duration

Abstract The South China block has been one of the most seismically quiescent regions in China, and the geometries and activities of the Quaternary faults have remained less studied due to the limited outcrops. Thus, source parameters of small-to-moderate earthquakes are important to help reveal the location, geometry distribution, and mechanical properties of the subsurface faults and thus improve the seismic risk assessment. On 12 October 2019, two earthquakes (the Ms 4.2 foreshock and the Ms 5.2 mainshock) occurred within 2 s and are located in southern South China block, near the junction region of the large-scale northeast-trending fault zones and the less continuous northwest-trending fault zones. We determined the point-source parameters of the two events via P-wave polarity analysis and regional waveform modeling, and the resolved focal mechanisms are significantly different with the minimum 3D rotation angle of 52°. We then resolved the rupture directivity of the two events by analyzing the azimuth variation of the source time duration and found the Ms 4.2 foreshock ruptured toward north-northwest for ∼1.0 km, and the Ms 5.2 mainshock ruptured toward east-southeast (ESE) for ∼1.5 km, implying conjugate strike-slip faulting. The conjugate causative faults have not been mapped on the regional geological map, and we infer that the two faults may be associated with the northwest-trending Bama-Bobai fault zone (the Shiwo section). These active faults are optimally oriented in the present-day stress field (northwest-southeast) and thus may now be potentially accumulating elastic strain to be released in a future large earthquake.

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

scholarly journals A New Signal Representation Using Complex Conjugate Pair Sums

2019 ◽  
Vol 26 (2) ◽  
pp. 252-256 ◽  
Author(s):  
Basheeruddin Shah Shaik ◽  
Vijay Kumar Chakka ◽  
Arikatla Satyanarayana Reddy
Keyword(s):  
Complex Conjugate ◽  
Signal Representation ◽  
Conjugate Pair ◽  
Complex Conjugate Pair
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