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### A simple mechanical model to analyse the rocking and sliding response of rigid blocks to earthquakes

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In order to study the effects of earthquakes on tombstones and monumental columns in recent years the dynamical analysis of rigid blocks subjected to ground accelerations has interested many researchers. Mainly, the rocking motion has been investigated and many numerical difficulties have been pointed out in such analysis [1-2-3-4]. Some computational advantages can be obtained by modelling the bonding between two blocks or between block and foundation by means of an elastic layer of Winkler's springs...

### Higher-order splitting method for elastic wave propagation.

International Journal of Mathematics and Mathematical Sciences

### Mathematical and numerical analysis of a stratigraphic model

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of $L$ lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness $h$, the $L$ surface concentrations ${c}_{i}^{s}$ in lithology $i$ of the sediments at the top...

### Mathematical and numerical analysis of a stratigraphic model

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h, the L surface concentrations ${c}_{i}^{s}$ in lithology i of the sediments at the...

### Mathematical modelling of rock bolt systems. II

Applications of Mathematics

The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied.

### New unilateral problems in stratigraphy

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type $0\in {\partial }_{t}u-div\left\{H\left({\partial }_{t}u+E\right)\nabla u\right\}$, where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...

### Non linear phenomena in glaciology: ice-surging and streaming.

RACSAM

En estas notas presentamos algunos modelos físicos que han sido propuestos recientemente para tratar el problema de los movimientos repentinos y casi periódicos del hielo, así como la aparición de corrientes de hielo rápidas en los grandes mantos glaciares que se deslizan sobre lechos blandos y deformables. Estos fenómenos están relacionados con la transición de un régimen de flujo lento a uno rápido y pueden aparecer debido a una modificación del sistema de drenaje del glaciar. Los fenómenos en...

### Numerical simulation of fractal interface effect of mining-caused activation of fault.

Discrete Dynamics in Nature and Society

### Numerical simulations through first order nonlinear difference equation to study highly ductile symmetric fold (HDSF) dynamics: A conceptual study.

Discrete Dynamics in Nature and Society

### On the Signorini problem with friction in linear thermoelasticity: The quasi-coupled 2D-case

Aplikace matematiky

The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary ${\Gamma }_{\alpha }$ of a polygonal domain $G\subset {R}^{2}$ is given. The rate of convergence is proved if the exact solution is sufficiently regular.

### Preconditioning of nonsymmetric saddle point systems as arising in modelling of viscoelastic problems.

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

### Rayleigh wave scattering at the foot of a mountain.

International Journal of Mathematics and Mathematical Sciences

### Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface.

International Journal of Mathematics and Mathematical Sciences

### Reflection and transmission of seismic waves under initial stress at the earth's core-mantle boundary.

International Journal of Mathematics and Mathematical Sciences

### Seismic inversion for a crak opening

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The displacement field caused by the classic earthquake mechanism model consisting of a slip along the fault is extended to the case when besides the slip, also an opening occurs caused by tensional forces. The tensor matrix describing the moment tensor does not necessarily have a nil trace. The direct problem is solved finding the radiation pattern for $P$ and $S$ waves. A method to solve the inverse problem of the determination of the four parameters describing the source is presented and tested on...

### The kinematic and dynamic properties of seismic waves in the neighbourhood of caustics

Acta Universitatis Carolinae. Mathematica et Physica

### The weak boundary effect in a field as a source approaches the boundary.

Journal of Mathematical Sciences (New York)

### Theoretical aspects of a multiscale analysis of the eigenoscillations of the Earth.

Revista Matemática Complutense

The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....