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1

Release-Rebound Processes : Vector Motions

Teisseyre R.

Acta Geophysica

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2015

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Vol. 63, no. 2

374--384

EN

The tensor relations describing the shear deviatoric strains and rotation strains may be presented as vector relations in a special coordinate system, e.g., in the diagonal or off-diagonal one. However, these fields can be also presented in the 4D invariant forms by means of invariant Dirac tensors. We present 4D relativistic relations for the invariant shear deviatoric strain and rotation strain vectors closely related to a fracture process in solids and to the molecular strains (shear and rotational) in fluids. These shear and rotation strains may interact with the radial derivatives of pressure along the propagation directions.

2

Thermodynamics with rotation motions: Fragmentation and slip

Majewski E., Teisseyre R.

Acta Geophysica

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2013

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Vol. 61, no. 2

281--310

EN

Basing on the Asymmetric Continuum Theory, we develop the thermodynamics including fragmentation spin fracture processes; applications for the earthquake source processes are considered. The fracture band model is used to describe a dislocation and disclination superlattice. The Gibbs free energy of defect formation is specified. A dynamic spin fracture criterion was formulated. Consequently, a dynamic model of rock fracture employing dislocations, disclinations, and cracks was constructed to describe slip and fragmentation fracture processes in the earthquake sources.

3

Molecular transport in fracture processes

Teisseyre R.

Acta Geophysica

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2013

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Vol. 61, no. 1

18--25

EN

The Asymmetric Continuum Theory based on deformation fields includes the strain rotation as an equally important deformation part as the shear and confining strains; all these fields can be related to their origin in the fracture processes by some displacement motions in a source. Some of these motions may belong to an individual process, some to complex correlated events ; in this latter case the displacements related to these strains could be shifted in phase. Moreover, we may expect an appearance of some molecular transport motions; the molecular transport may be helpful for understanding an interaction of the molecular processes and related molecular momentum flux. These correlated events should be mutually related in a source by the release-rebound mecha- nism. In particular, we consider the point fracture events as associated with a confining load or /and with the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. It is to be pointed out that such molecular motions are too small to be observed by the existing seismological networks.

4

Induced strains and defect continuum theory: Internal reorganization of load

Teisseyre R., Górski M.

Acta Geophysica

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2012

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Vol. 60, no. 1

24-42

EN

Induced strains play an important role in mining regions and water dam areas. We consider a mechanism of reorganization of the applied stress load by some changes in rock-body defect distribution caused by human activity. A defect content increases with increasing stress load and related deformations; hence, a relationship could appear between seismic risk and deformation level. Recent progress in the Asymmetric Continuum Theory permits to consider some internal reorganization of the applied load due to internal defect content and distribution; in this paper we consider an increase of internal defect densities due to mining works and the appearance of reorganized internal stress distribution. A generalization of the Peach–Koehler forces acting on the defects makes it possible to define formation of induced strains; a character of resulting strains may essentially differ from the applied load. In the case of an axial load, this approach helps to understand formation of shear or rotational micro-fractures, usually recognized as fragmentation and slip motions.

5

Earthquake fragmentation and slip processes: spin and shear-twist wave mosaic

Teisseyre R., Górski M.

Acta Geophysica

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2011

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Vol. 59, no. 3

453-469

EN

We followour former considerations on rotational processes and emission of rotation and shear-twist waves as occurring in earthquake source zones. A concise presentation of the motion and constitutive relations is given for each type of the four fundamental point deformations: displacements, rotations, point stretch/squeeze, and string-string point deformations (shear nuclei). We apply the Asymmetric Continuum Theory to the micro-fracture processes in an earthquake source zone: the fragmentation and slip processes are described by the linear and rotational transport fields incorporated in the motion equations. The advanced non-linear micro-fracture processes under high load are discussed.

6

Fluid theory with asymmetric molecular stresses: Difference between vorticity and spin equations

Teisseyre R.

Acta Geophysica

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2010

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Vol. 58, no. 6

1056-1071

EN

We present a new development in fluid theory, incorporating into it the velocity and spin fields; special attention is given to the structure of transport.The theory includes asymmetric molecular stresses and independent rotation velocity, i.e., spin. Our approach is based on our former studies on the asymmetric continuum theory with the balance and constitutive laws for displacement velocity and independent rotation motion, and points out the role of a related characteristic length unit. It is assumed that the vorticity caused by velocities can induce a spin transport counterpart. Thus, under certain conditions, an additional transport term due to rotational velocity fields may be incorporated to the velocity transport, which may lead to the vortex fields included directly into the theory. The Coriolis effect, important for the vortex processes, is considered and it is demonstrated that the motion equations in our asymmetric theory include this effect automatically. When confinining to 2D case, some compatibilities are found between the relations derived for the rotation motions and the moment formed by the Coriolis forces and applied to such motions. This is an important argument supporting our approach. The obtained nonlinear vortex equations (solitons) are derived and discussed for a stationary case.

7

Transport in fracture processes: Fragmentation and slip

Teisseyre R., Górski M.

Acta Geophysica

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2009

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Vol. 57, no. 3

583-599

EN

We present a new development in the asymmetric continuum theory with the shear oscillations (twist motions) and independent spin; these motions (displacement velocities and spin) can be shifted in phase to describe the independent rebound processes. Our approach provides an extension of the asymmetric continuum theory by including the microfragmentation processes with a double transport which may appear in an advanced fracture process under very high load. The related nonlinear equations, leading to soliton solutions, are derived.

8

Introduction to asymmetric continuum: dislocations in solids and extreme phenomena in fluids

Teisseyre R.

Acta Geophysica

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2008

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Vol. 56, no. 2

259-269

EN

We present a new approach to the continuum theories: for solids, our version includes the asymmetric stresses, symmetric strains and antisymmetric rotations, while for fluids we take the similar assumptions but related to the respective time rates of these fields. We consider the constitutive relations and the balance laws: those related to the antisymmetric stresses are equivalent and substitute the required relations for the angular moment; a similar approach with rates of these fields is applied for fluids. The stress-dislocation relations are derived and the role of rotation motions in the fracture processes in solids is studied. A new theory of the extreme motion phenomena in fluids is developed.

9

Physics of basic motions in asymmetric continuum

Teisseyre R., Górski M.

Acta Geophysica

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2007

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Vol. 55, no. 2

119-132

EN

We consider the advantages of a formalism based on concept of the asymmetric continuum and we present some equivalence theorems relating it to the asymmetric elasticity and to micropolar and micromorphic theories as founded by Nowacki, Cosserats and Eringen. We consider the basic processes in an asymmetric continuum which could be reduced to the point basic motions/deformations. The coaction of spin and shear motions is assumed to play the main role in fracturing process, while the constitutive relation between the antisymmetric stresses and rotations replaces the friction constitutive law.

10

Asymmetric Continuum and Anisotropy

Teisseyre R.

Acta Geophysica

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2006

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Vol. 54, no. 3

225-238

EN

We present a relation between stress moments and antisymmetric part of stresses and the related constitutive law joining those stresses with the particle/point rotations. Correspondence of the asymmetric continuum theory to the micromorphic theory is considered. An extension of the asymmetric continuum theory for the case of 2D anisotropy for antisymmetric stresses leads us to the problems of friction ani-sotropy and fracture pattern.

11

Usefulness of the fiber-optic interferometer for the investigation of the seismic rotation waves

Jaroszewicz L., Krajewski Z., Teisseyre R.

Optica Applicata

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2005

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Vol. 35, nr 2

383-394

EN

In the paper new areas of the fiber-optic Sagnac interferometer applications are discussed and proposed. Because this system detects the absolute rotation, its application is directly designed for detection of the seismic rotation waves which are rotational events existing in the seismic waves. In most cases those waves are extracted from recordings of differential seismic signals. However, all differences in responses of the seismometers cause disturbances which obscure these hidden components as it is for two antiparallel pendulum seismometers (TAPS) system. The presented device, named fiber-optic rotational seismometer (FORS), is free from this disadvantage and may be used for other rotational seismometer calibration, as well as for direct seismic rotation waves detection. The paper describes the design based on a well-known optical gyroscope configuration but with its optimization for its optimization for detection the absolute rotation, only. The obtained results have been the source of TAPS work improvement by applying the data smoothing by a spline function. Moreover, the first application of FORS for recording rotational parts existing in the seismic events has shown that they probably propagate with different velocity than classical earthquake waves.

12

Degenerated mechanics in a homogeneous continuum: potentials for spin and twist

Teisseyre R., Białecki M., Górski M.

Acta Geophysica Polonica

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2005

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Vol. 53, nr 3

219-230

EN

In this paper we extend our considerations on the spin and twist motions in a homogenous continuum. Refering to our former results, we define the degenerated mechanics as that in which the displacement motions vanish while rotation motions, as the independent elastic fields, do exist. This is exactly the opposite case to the classic ideal elastic continuum in which only displacement motions are taken into account, while any independent rotation motions are excluded because of a lack of the appriopriate constitutive laws supporting the existence of an elastic response due to the rotational deformations of bonds in a lattice network. We propose a system of potentials which would help us to understand the waves and geometrical features of degenerated mechanics and its Riemannian geometry.

13

Asymmetric continuum mechanics: deviations from elasticity and symmetry

Teisseyre R.

Acta Geophysica Polonica

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2005

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Vol. 53, nr 2

115-126

EN

The Kröner approach to continua with a distribution of self-field sources is applied to a wide class of deviations from the classical ideal elasticity; the same approach is applied to the theory of continua with asymmetric fields. The corresponding equations of motion are derived. Such an approach replaces other methods based on the constitutive relations specific for each type of the medium; here, the reference constitutive relation remains the same, but deviations from the classical ideal elasticity are attributed to different sources and defects introduced into continuum theory. Both methods lead to the expressions for the related currents. The nuclei responsible for the deviations from classical elasticity can be related to the defect distribution (dislocation and disclination densities), thermal excitation, some features of internal structure and different types of nuclei (e.g. electric nuclei, rotation nuclei); other deviations lead to an elastoplastic behavior. Our considerations extend also on deviations from the stress symmetry and related incompatibilities; we consider the resulting equations of motion.

14

Zwężka do pomiaru częściowego strumienia masy w transporcie pneumatycznym pyłu węglowego w energetyce / Mieczysław Teisseyre [i in.]

Teisseyre M., Mazur M., Rydz W., Teisseyre R.

Inżynieria Chemiczna i Procesowa

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2004

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T. 25, z. 4

2367-2374

PL

Podano zasadę działania przyrządu pomiarowego, o umownej nazwie "sonda Y[q]. do monitorowania rozpływu mieszanki paliwowej (powietrze - pył węglowy) zasilającej palniki kotłów energetycznych. W niestosowanym dotychczas rozwiązaniu funkcjonalno-konstrukcyjnym wykorzystano zasadę zwężki trójsygnałowej (metoda Graczyka) oraz sondy zerowej (zasada Allena), Zaprezentowano wyniki wzorcowania przyrządu na zbudowanym do tego celu stanowisku doświadczalnym. Przeprowadzono wstępną ocenę przyrządu i metody pomiaru.

EN

The principle of a device operation, called as "the probe Y[q]", for monitoring of fuel mixture (air-pulverized coal) distribution in a coal-fired power station is presented. In the non-conventional functional-constructional solution are used of the Graczyk method and the Allen principle. The results of the probe Y[q] calibration in laboratory stand are presented. The initial assessment about the device and the measuring method is done.

15

Sejsmiczne efekty rotacyjne

Teisseyre R.

Geologia / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2004

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T. 30, z. 3

249-263

16

Spin and twist motions in a homogeneous elastic continuum and cross-band geometry of fracturing

Teisseyre R.

Acta Geophysica Polonica

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2004

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Vol. 52, nr 2

173-183

EN

A uniform continuum with rotation motions of spin and twist type is presented; in this approach we supplement the ideal elasticity constitutive law, the strain-stress relation, by the rotation-asymmetric stress relation. In such a way, we can evade an influence of the Hook law, which, when used as the unique law in the ideal elasticity, rules out an existence of rotation waves. Thus, in the ideal elastic continuum the rotation vibrations can propagate and are not attenuated. The asymmetric elastic rotation fields and their relation to asymmetric elastic stresses are proposed and discussed, under the condition that the total fields with the elastic and self parts remain symmetric or antisymmetric as required by the compatibility conditions. The tensor of incompatibility splits into the symmetric or antisymmetric parts. The conservation and balance laws for spin and twist fields and the stress -related equations of motion for symmetric and antisymmetric parts of stresses are given. The relations obtained for elastic fields, expressed by difference of the total and self-fields, can be split into the self-parts prevailing on the fracture plane and the total parts describing seismic radiation field in a surrounding space. The role of rotation processes in premonitory and rebound time domains is considered in estimating the most effective fracture patterns.

17

Generalized continuum with defects and asymmetric stresses

Boratyński W., Teisseyre R.

Acta Geophysica Polonica

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2004

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Vol. 52, nr 2

185-195

EN

Consistent theory is presented of continuum with defect distribution: dislocation and disclination densities and the densities of rotation nuclei of two kinds. Special attention is paid to rotation and twist motions, and the two approaches to the definition of the twist-bend tensor are combined. The elastic and self fields of stresses and strains become asymmetric, while the total fields remain symmetric as required by the compatibility conditions. However, the tensor of incompatibility becomes asymmetric. The dislocation-stress relations and the equations of motion for symmetric and asymmetric parts of stresses are given and the wave equations for spin and twist are derived. Some applications are shortly discussed.

18

Electromagnetic excitation and seismicity in the natural time domain: simulations with theoretical model

Teisseyre R., Varotsos P., Rozłuski C.

Acta Geophysica Polonica

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2004

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Vol. 52, nr 4

477-496

EN

Numerical simulations of electromagnetic field and electric current are based on the solutions of equations for the dislocation density field with the term including self-interactions between the dislocations; the case under study concerns the charge dislocations. The equations are solved numerically for the medium with thin layers representing the faults and for the initial conditions representing two groups of dislocations of opposite signs facing each other. This case refers to stress concentration; the gradients of stress field, opposite to the central point of stress accumulation, contribute to the respective dislocation densities since the linear dislocation density for a simple 1D case becomes proportional to stress gradient. A single fault, as a zone with small resistance/friction values, is described by rigidities smaller than the bulk rigidity value, while for a fine-band structure of faults the rigidities in the layers between the adjacent faults are assumed to be higher than the bulk value. The results obtained show characteristic features in which the seismic precursory activity simulates that of the main rebound processes represented in the natural time as counted in relation to the consecutive events. Our model contributes to the previous discussion and experimental data related to natural time analysis suggested recently by Varotsos and coworkers.

19

Seismic rotation waves related to volcanic, mining and seismic events: Near-field and micromorphic motions

Teisseyre R., Teisseyre K., Moriya T., Palangio P.

Acta Geophysica Polonica

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2003

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Vol. 51, nr 4

409-431

EN

Rotation and twist waves recorded in Hokkaido (Japan), Ojców and Książ (Poland) and L'Aquila (Italy) bring a new insinght into the features of these motions for volcanic, mining and tectonic events. The rotation seismograph system used at the observatories in Hokkaido differs from that observatories in Poland and Italy. Nevertheless, the results obtained, for all observatories, are compatible. The levels of rotation and twist motions depend distinctly on the back-ground properties of the recording sited. Moreover, at a given recording station we have noticed two different levels of these motions; for some near events the records indicate very small rotation motions, while for other, also near events, these motions are distinctly greater and remain on a similar level as those for records from the distant sources. For the near events the evident differences in magnitudes and character of these motions suggest a distinct relation between the rotation and twist motions and the source mechanism. Similarly, an analysis of records for the volcanic events indicates existence of two kinds of events: for the first group, the rotation components reach the order of magnitude much greater than those for the group, for which the rotation and twist motions are quite negligible. The records related to this group, representing probably the near-surface volcanic explosions, confirm at the same time the reliability of results obtained for the rotation motions belonging to the first group, as the technique of recording and distances remain for both groups the same. The records from several stations give grounds for searching for as influence local structure on rotation and twist motions. The data treatment applied for local events made it possible to separate the recorded motions into the micromorphic and source related parts.

20

Recording the seismic rotation waves: reliability analysis

Teisseyre R., Suchcicki J., Teisseyre K.

Acta Geophysica Polonica

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2003

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Vol. 51, nr 1

37-50

EN

An estimation of reliability of seismic rotation waves is based on the data collected with the use of rotation horizontal seismographs; each rotation seismograph system consists of two anti-parallel seismographs. The test and working positions of the rotation seismographs enable us to use the filtering procedure in the FFT domain in order to approach the identity of seismograph responses for each system; this procedure is applied for the collected data. Reliability of records of seismic rotation waves is based on the estimated ranges of the mean square values of the errors (test position) and of the rotation and twist components (working position). In this way, we get a proof about the existence of seismic rotation waves, at least those rotation components of seismic waves which originate near the surface and close to the observation site. This proof may be very important for the earthquake engineering problems. The question of a possibility of reducing far-distance rotation effects, as those related to seismic source process, remains open.