Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics

In the present paper, we propose a new model for landslide dynamics, in the form of the spring-block mechanical model, with included delayed interaction and the effect of the background seismic noise. The introduction of the random noise in the model of landslide dynamics is confirmed by the surrogate data testing of the recorded ambient noise within the existing landslide in Serbia. The performed research classified the analyzed recordings as linear stationary stochastic processes with Gaussian inputs. The proposed mechanical model is described in the form of a nonlinear dynamical system: a set of stochastic delay-differential equations. The solution of such a system is enabled by the introduction of mean-field approximation, which resulted in a mean-field approximated model whose dynamics are qualitatively the same as the dynamics of the starting stochastic system. The dynamics of the approximated model are analyzed numerically, with rather unexpected results, implying the positive effect of background noise on landslide dynamics. Particularly, the increase of the noise intensity requires higher values of spring stiffness and displacement delay for the occurrence of bifurcation. This confirms the positive stabilizing effect of the increase in noise intensity on the dynamics of the analyzed landslide model. Present research confirms the significant role of noise in landslides near the bifurcation point (e.g., creeping landslides)

Supplementary material for: Prekrat, D., Todorović-Vasović, K. N., Vasović, N.,& Kostić, S.. (2024). Complex global dynamics of conditionally stable slopes: effect of initial conditions. in Frontiers in Earth Science Frontiers Media., 12 - 2024 https://doi.org/10.3389/feart.2024.1374942

In the present paper, we investigate the effect of the initial conditions on the dynamics of the spring-block landslide model. The time evolution of the studied model, which is governed by a system of stochastic delay differential equations, is analyzed in the mean-field approximation, which qualitatively exhibits the same dynamics as the initial model. The results of the numerical analysis show that changing the initial conditions has different effects in different parts of the parameter space of the model. Namely, moving away from the fixed-point initial conditions has a stabilizing effect on the dynamics when the noise, the friction parameters a (higher values) and c as well as the spring stiffness k are taken into account. The stabilization manifests itself in a complete suppression of the unstable dynamics or a partial limitation of the effect of some friction parameters. On the other hand, the destabilizing effect of changing the initial conditions occurs for the lower values of the friction parameters a and for b. The main feature of destabilization is the complete suppression of the sliding regime or a larger parameter range with a transient oscillatory regime. Our approach underlines the importance of analyzing the influence of initial conditions on landslide dynamics.Supplementary material for: [https://doi.org/10.3389/feart.2024.1374942]Related to published version: [https://farfar.pharmacy.bg.ac.rs/handle/123456789/5561

Nonlinear time series analysis of fluid dynamics: stohastic groundwater level oscillation

In present paper we analyze dynamics of groundwater level oscillation recorded at two piezometric stations in Pancevacki rit: ‘’Cuvarnica’’, and ‘’Borca’’ in period 2007-2013. Primary goal of the performed research was to determine the character of the main mechanism behind these oscillations, which could further serve as a solid base for creating an appropriate prediction model. Dynamics of the recorded time series is examined using methods of nonlinear time series analysis and delay embedding theorem. After embedding the observed time series into three dimensional phase space with embedding delay τ=4, results of surrogate data testing showed that analyzed time series originate from a stationary Gaussian linear process that could be distorted by a monotonic, instantaneous, time-independent nonlinear function. This is further confirmed by low values of determinism coefficient and corresponding vector field composed of vectors of different length, indicating high level of stochasticity in the observed data. The obtained results provide solid foundation for future research, with the final goal of creating an appropriate prediction model

Periodic and autoregressive models of groundwater level dynamics

In this paper, authors examine the groundwater level oscillation at groundwater station Bogatić near Šabac (Serbia), for the period 2002-2014. Analysis is done by transforming the observation data into Fourier series within fundamental period of 5 years, and by deriving a model based on the autocorrelation properties of the recorded data. One should note that this is the first time that such analyzes are preformed for the groundwater level oscillation observed in Serbia. The derived model based on groundwater level periodicity is represented by a combination of sine and cosine waves. Analysis shows rather satisfying statistical accuracy of the model, with R 2=0.707 and mean absolute error of 0.34m, which fails to capture the highest values of the groundwater level for the analyzed period. Second model is expressed in a form of a simple correlation between the two successive observations, with a time delay τ=1 and 4. Both models are derived for the period 2003-2009, and their prediction accuracy is checked for the period 2010-2014. Both of these models provide more accurate predictions in comparison to the model based on the groundwater level periodicity

Stavovi, znanje i praksa negovatelja u održavanju oralnog zdravlja korisnika domova za stara lica u Srbiji

Background/Aim. Within the elderly population, residents in nursing homes, there is a greather risk of caries, periodontal disease and teeth loss. Assistance of caregivers in maintaininig good oral hygiene besides improving oral health can improve of residents general health and the quality of their lives. The aim of this study was to examine the attitudes of caregivers and knowledge about oral health, as well as the practice regarding oral care they apply at nursing homes in Serbia. Methods. The survey was conducted at the Gerontology Center Belgrade, consisting of four nursing homes located in the urban area. The study included 58 caregivers. They were contacted on working days, in all work shifts, during January, February and March of 2013. They were asked to fill in a self-administered questionnaire consisting of 26 closed-type questions. Results. The care-givers mostly considered that it was very important to take care of oral health of the residents, but 69% responded that the level of their oral health was low or very low. As the main barriers to oral hygiene maintenance, the caregivers indicated lack of time. The caregivers had more knowledge about periodontal disease than about the main cause of caries and its prevention. Formal medical education had the influence on the knowledge about oral diseases. Oral hygiene procedures carried out by the mayority of caregivers were denture cleaning and tooth brushing. Conclusion. The caregivers were aware of the limitations in everyday oral care of nursing homes residents in Serbia, although solving these problems requires the involvement of the entire public health service.Uvod/Cilj. U grupi starijih osoba, stanovnika domova za stara lica, postoji povećani rizik od nastanka karijesa, periodontalne bolesti i gubitka zuba. Pomoć u održavanju dobre oralne higijene, pored toga, može uticati i na opšte zdravstveno stanje i kvalitet života stanovnika domova za stara lica. Cilj ovog istraživanja bio je da se ispitaju stavovi i znanje negovatelja o oralnom zdravlju, kao i praksa koju primjenjuju u domovima za stara lica u Srbiji. Metode. Istraživanje je sprovedeno u ustanovi Gerontološki Centar Beograd, koji se sastoji od četiri doma za stara lica, locirana u urbanom području. U istraživanju je učestvovalo 58 negovatelja, s kojima smo kontaktirali radnim danima, u svim radnim smenama, tokom januara, februara i marta 2013. godine. Oni su zamoljeni da samostalno ispune upitnik sastavljen od 26 pitanja zatvorenog tipa. Rezultati. Negovatelji uglavnom smatraju da je veoma važno brinuti se o oralnom zdravlju korisnika domova, ali 69% je odgovorilo da je nivo oralnog zdravlja korisnika nizak ili vrlo nizak. Za glavnu prepreku u održavanju oralne higijene korisnika domova, negovatelji su označili nedostatak vremena. Njegovatelji su imali više znanja o parodontalnim bolestima, nego o glavnom uzročniku karijesa i njegovoj prevenciji. Formalno medicinsko obrazovanje imalo je uticaj na njihovo znanje o oralnim bolestima. Čišćenje proteza i pranje zuba su najčešće primenjivani postupci negovatelja u održavanju oralne higijene korisnika domova. Zaključak. Negovatelji su svesni ograničenja u svakodnevnom održavanju oralnog zdravlja korisnika domova za stara lica u Srbiji, kao i da rešavanje tih problema zahteva uključivanje celokupnog javnog zdravstvenog sektora

Nonlinear time series analysis of fluid dynamics: stohastic groundwater level oscillation

In present paper we analyze dynamics of groundwater level oscillation recorded at two piezometric stations in Pancevacki rit: ‘’Cuvarnica’’, and ‘’Borca’’ in period 2007-2013. Primary goal of the performed research was to determine the character of the main mechanism behind these oscillations, which could further serve as a solid base for creating an appropriate prediction model. Dynamics of the recorded time series is examined using methods of nonlinear time series analysis and delay embedding theorem. After embedding the observed time series into three dimensional phase space with embedding delay τ=4, results of surrogate data testing showed that analyzed time series originate from a stationary Gaussian linear process that could be distorted by a monotonic, instantaneous, time-independent nonlinear function. This is further confirmed by low values of determinism coefficient and corresponding vector field composed of vectors of different length, indicating high level of stochasticity in the observed data. The obtained results provide solid foundation for future research, with the final goal of creating an appropriate prediction model

Periodic and autoregressive models of groundwater level dynamics

In this paper, authors examine the groundwater level oscillation at groundwater station Bogatić near Šabac (Serbia), for the period 2002-2014. Analysis is done by transforming the observation data into Fourier series within fundamental period of 5 years, and by deriving a model based on the autocorrelation properties of the recorded data. One should note that this is the first time that such analyzes are preformed for the groundwater level oscillation observed in Serbia. The derived model based on groundwater level periodicity is represented by a combination of sine and cosine waves. Analysis shows rather satisfying statistical accuracy of the model, with R 2=0.707 and mean absolute error of 0.34m, which fails to capture the highest values of the groundwater level for the analyzed period. Second model is expressed in a form of a simple correlation between the two successive observations, with a time delay τ=1 and 4. Both models are derived for the period 2003-2009, and their prediction accuracy is checked for the period 2010-2014. Both of these models provide more accurate predictions in comparison to the model based on the groundwater level periodicity

Mechanics of weathered clay-marl rock masses along the rupture surface in homogeneous dry slopes

Authors analyze stress-strain distribution within slope using the shear stress reduction technique based on finite element method, which was previously confirmed to provide approximately the same results as the Janbu's corrected limit equilibrium method. Results obtained indicate that the largest vertical displacements occur at the slope base and crest, while central part of the slope is exposed to the largest horizontal displacements. Normal and shear stress show maximum values in the middle part of the slope. It was also determined that separate stress-strain relations could be derived for the exact upper and lower part of the rupture surface

Triggered dynamics in a model of different fault creep regimes

The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic-or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale

Mean field approximation for noisy delay coupled excitable neurons

Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by $N\gg 1$ stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.Comment: 15 pages, 3 figure