Prolonged drought periods over the last four decades increase flood intensity in southern Africa

In semi-arid sub-Saharan Africa, climate change and the intensification of human activities have altered the hydrological balance and modified the recurrence of extreme hydroclimatic events, such as droughts and floods. The geomorphological heterogeneity of river catchments across the region, the variable human pressure, and the lack of continuous hydroclimatic data preclude the definition of proper mitigation strategies, with a direct effect on the sustainability of rural communities. Here, for the first time in Africa, we characterize hydrological extreme events using a multidisciplinary approach that includes sedimentary data from dams. We focus on the Limpopo River basin to evaluate which factors control flood magnitude since the 1970. Extreme flood events were identified across the basin in 1988-89, 1995-96, 1999-2000, 2003-04, 2010-11, 2013-14 and 2016-17. The statistical analysis of sedimentary flood records revealed a dramatic increase in their magnitude over the studied period. A positive correlation between maximum river flow and antecedent prolonged drought conditions was found in South Africa and Mozambique. Most importantly, since 1980, we observed the likely decoupling of extreme floods from the magnitude of La Niña events, suggesting that the natural interannual variability driven by El Niño-Southern Oscillation (ENSO) has been disrupted by climate changes and human activities.

Quantifying heterogeneity in ecohydrological partitioning in urban green spaces through the integration of empirical and modelling approaches

Urban green spaces (UGS) can help mitigate hydrological impacts of urbanisation and climate change through precipitation infiltration, evapotranspiration and groundwater recharge. However, there is a need to understand how precipitation is partitioned by contrasting vegetation types in order to target UGS management for specific ecosystem services. We monitored, over one growing season, hydrometeorology, soil moisture, sapflux and isotopic variability of soil water under contrasting vegetation (evergreen shrub, evergreen conifer, grassland, larger and smaller deciduous trees), focussed around a 150-m transect of UGS in northern Scotland. We further used the data to develop a one-dimensional model, calibrated to soil moisture observations (KGE's generally > 0.65), to estimate evapotranspiration and groundwater recharge. Our results evidenced clear inter-site differences, with grassland soils experiencing rapid drying at the start of summer, resulting in more fractionated soil water isotopes. Contrastingly, the larger deciduous site saw gradual drying, whilst deeper sandy upslope soils beneath the evergreen shrub drained rapidly. Soils beneath the denser canopied evergreen conifer were overall least responsive to precipitation. Modelled ecohydrological fluxes showed similar diversity, with median evapotranspiration estimates increasing in the order grassland (193 mm) < evergreen shrub (214 mm) < larger deciduous tree (224 mm) < evergreen conifer tree (265 mm). The evergreen shrub had similar estimated median transpiration totals as the larger deciduous tree (155 mm and 128 mm, respectively), though timing of water uptake was different. Median groundwater recharge was greatest beneath grassland (232 mm) and lowest beneath the evergreen conifer (128 mm). The study showed how integrating observational data and simple modelling can quantify heterogeneities in ecohydrological partitioning and help guide UGS management.

Synapse-Specific Modulation of Synaptic Responses by Brain States in Hippocampal Pathways

Synaptic changes play a major role in memory processes. Modulation of synaptic responses by brain states remains, however, poorly understood in hippocampal networks, even in basal conditions. We recorded evoked synaptic responses at five hippocampal pathways in freely moving male rats. We showed that, at the perforant path to dentate gyrus (PP-DG) synapse, responses increase during wakefulness compared with sleep. At the Schaffer collaterals to CA1 (SC-CA1) synapse, responses increase during non-REM sleep (NREM) compared with the other states. During REM sleep (REM), responses decreased at the PP-DG and SC-CA1 synapses compared with NREM, while they increased at the fornix to nucleus accumbens synapse (Fx-NAc) during REM compared with the other states. In contrast, responses at the fornix to medial PFC synapse (Fx-PFC) and at the fornix to amygdala synapse (Fx-Amy) were weakly modulated by vigilance states. Extended sleep periods led to synaptic changes at PP-DG and Fx-Amy synapses but not at the other synapses. Synaptic responses were also linked to local oscillations and were highly correlated between Fx-PFC and Fx-NAc but not between Fx-Amy and these synapses. These results reveal synapse-specific modulations that may contribute to memory consolidation during the sleep-wake cycle.SIGNIFICANCE STATEMENT Surprisingly, the cortical network dynamics remains poorly known at the synaptic level. We tested the hypothesis that brain states would modulate synaptic changes in the same way at different cortical connections. To tackle this issue, we implemented an approach to explore the synaptic behavior of five connections upstream and downstream the rat hippocampus. Our study reveals that synaptic responses are modulated in a highly synapse-specific manner by wakefulness and sleep states as well as by local oscillations at these connections. Moreover, we found rapid synaptic changes during wake and sleep transitions as well as synaptic down and upregulations after extended periods of sleep. These synaptic changes are likely related to the mechanisms of sleep-dependent memory consolidation.

Occurrence of methane-oxidizing bacteria and methanogenic archaea in earth’s cave systems—A metagenomic analysis

Karst ecosystems represent up to 25% of the land surface and recent studies highlight their potential role as a sink for atmospheric methane. Despite this, there is limited knowledge of the diversity and distribution of methane-oxidizing bacteria (MOB) or methanogens in karst caves and the sub-surface environment in general. Here, we performed a survey of 14 shotgun metagenomes from cave ecosystems covering a broad set of environmental conditions, to compare the relative abundance and phylogenetic diversity of MOB and methanogens, targeting biomarker genes for methane monooxygenase (pmoA and mmoX) and methyl-coenzyme M reductase (mcrA). Taxonomic analysis of metagenomes showed 0.02–1.28% of classified reads were related to known MOB, of which Gammaproteobacterial MOB were the most abundant making up on average 70% of the surveyed caves’ MOB community. Potential for biogenic methane production in caves was also observed, with 0.008–0.39% of reads classified to methanogens and was dominated by sequences related to Methanosarcina. We have also generated a cave ecosystems protein database (CEPD) based on protein level assembly of cave metagenomes that can be used to profile genes of interest.

Defects in Mouse Cortical Glutamate Uptake Can Be Unveiled In Vivo by a Two-in-One Quantitative Microdialysis

Extracellular glutamate levels are maintained low by efficient transporters, whose dysfunction can cause neuronal hyperexcitability, excitotoxicity, and neurological disease. While many methods estimate glutamate uptake in vitro/ex vivo, a limited number of techniques address glutamate transport in vivo. Here, we used in vivo microdialysis in a two-in-one approach combining reverse dialysis of isotopic glutamate to measure uptake ability and zero-flow (ZF) methods to quantify extracellular glutamate levels. The complementarity of both techniques is discussed on methodological and anatomical basis. We used a transgenic mouse model of human disease, expressing low levels of the EAAT-2/GLT1 glutamate transporter, to validate our approach in a relevant animal model. As expected, isotopic analysis revealed an overall decrease in glutamate uptake, while the ZF method unveiled higher extracellular glutamate levels in these mice. We propose a sensitive and expedite two-in-one microdialysis approach that is sufficiently robust to reveal significant differences in neurotransmitter uptake and extracellular levels through the analysis of a relatively low number of animals.

Working and Reference Memory Tasks Trigger Opposed Long-Term Synaptic Changes in the Rat Dentate Gyrus

Long-term storage of information into memory is supposed to rely on long-term synaptic plasticity processes. The detection of such synaptic changes after training in long-term/reference memory (RM) tasks has yet been scarce, variable and only studied on a short time scale. Short-term or working memory (WM) is largely known to depend on persistent neuronal activity or short-term plasticity. However, processing information into WM could also involve long-term synaptic changes that could be responsible for the erasure/forgetting of items previously stored in WM and acting as proactive interference. In order to study long-term synaptic changes associated with RM or WM, we trained chronically implanted rats in 3 different radial maze tasks: a classical RM task and 2 WM tasks involving different levels of proactive interference. Synaptic responses in the dentate gyrus were recorded during 2 × 24 h in freely moving rats after training. We found that consolidation of long-term information leads first to a delayed synaptic potentiation, occurring 9 h after RM training that is replaced by a synaptic depression once the RM rule is fully acquired. In contrast, optimal information processing into WM triggers a synaptic depression immediately after training and lasting 3 h that could act as a mechanism for interference erasure/forgetting.

Ketamine/xylazine and barbiturates modulate microglial morphology and motility differently in a mouse model

Microglia, the resident immune cells of the brain, are highly ramified and motile and their morphology is strongly linked to their function. Microglia constantly monitor the brain parenchyma and are crucial for maintaining brain homeostasis and fine-tuning neuronal networks. Besides affecting neurons, anesthetics may have wide-ranging effects mediated by non-neuronal cells and in particular microglia. We thus examined the effect of two commonly used anesthetic agents, ketamine/xylazine and barbiturates, on microglial motility and morphology. A combination of two-photon in vivo imaging and electroencephalography (EEG) recordings in unanesthetized and anesthetized mice as well as automated analysis of ex vivo sections were used to assess morphology and dynamics of microglia. We found that administration of ketamine/xylazine and pentobarbital anesthesia resulted in quite distinct EEG profiles. Both anesthetics reduced microglial motility, but only ketamine/xylazine administration led to reduction of microglial complexity in vivo. The change of cellular dynamics in vivo was associated with a region-dependent reduction of several features of microglial cells ex vivo, such as the complexity index and the ramification length, whereas thiopental altered the size of the cytoplasm. Our results show that anesthetics have considerable effects on neuronal activity and microglial morphodynamics and that barbiturates may be a preferred anesthetic agent for the study of microglial morphology. These findings will undoubtedly raise compelling questions about the functional relevance of anesthetics on microglial cells in neuronal physiology and anesthesia-induced neurotoxicity.

Differential recordings of local field potential: A genuine tool to quantify functional connectivity

Local field potential (LFP) recording is a very useful electrophysiological method to study brain processes. However, this method is criticized for recording low frequency activity in a large area of extracellular space potentially contaminated by distal activity. Here, we theoretically and experimentally compare ground-referenced (RR) with differential recordings (DR). We analyze electrical activity in the rat cortex with these two methods. Compared with RR, DR reveals the importance of local phasic oscillatory activities and their coherence between cortical areas. Finally, we show that DR provides a more faithful assessment of functional connectivity caused by an increase in the signal to noise ratio, and of the delay in the propagation of information between two cortical structures.

Highly Dynamic Spatiotemporal Organization of Low-Frequency Activities During Behavioral States in the Mouse Cerebral Cortex

Although low-frequency (LF < 10 Hz) activities have been considered as a hallmark of nonrapid eye movement (NREM) sleep, several studies have recently reported LF activities in the membrane potential of cortical neurons from different areas in awake mice. However, little is known about the spatiotemporal organization of LF activities across cortical areas during wakefulness and to what extent it differs during NREM sleep. We have thus investigated the dynamics of LF activities across cortical areas in awake and sleeping mice using chronic simultaneous local field potential recordings. We found that LF activities had higher amplitude in somatosensory and motor areas during quiet wakefulness and decreased in most areas during active wakefulness, resulting in a global state change that was overall correlated with motor activity. However, we also observed transient desynchronization of cortical states between areas, indicating a more local state regulation. During NREM sleep, LF activities had higher amplitude in all areas but slow-wave activity was only poorly correlated across cortical areas. Despite a maximal amplitude during NREM sleep, the coherence of LF activities between areas that are not directly connected dropped from wakefulness to NREM sleep, potentially reflecting a breakdown of long-range cortical integration associated with loss of consciousness.

Levels of Interference in Long and Short-Term Memory Differentially Modulate Non-REM and REM Sleep

STUDY OBJECTIVES

It is commonly accepted that sleep is beneficial to memory processes, but it is still unclear if this benefit originates from improved memory consolidation or enhanced information processing. It has thus been proposed that sleep may also promote forgetting of undesirable and non-essential memories, a process required for optimization of cognitive resources. We tested the hypothesis that non-rapid eye movement sleep (NREMS) promotes forgetting of irrelevant information, more specifically when processing information in working memory (WM), while REM sleep (REMS) facilitates the consolidation of important information.

METHODS

We recorded sleep patterns of rats trained in a radial maze in three different tasks engaging either the long-term or short-term storage of information, as well as a gradual level of interference.

RESULTS

We observed a transient increase in REMS amount on the day the animal learned the rule of a long-term/reference memory task (RM), and, in contrast, a positive correlation between the performance of rats trained in a WM task involving an important processing of interference and the amount of NREMS or slow wave activity. Various oscillatory events were also differentially modulated by the type of training involved. Notably, NREMS spindles and REMS rapid theta increase with RM training, while sharp-wave ripples increase with all types of training.

CONCLUSIONS

These results suggest that REMS, but also rapid oscillations occurring during NREMS would be specifically implicated in the long-term memory in RM, whereas NREMS and slow oscillations could be involved in the forgetting of irrelevant information required for WM.

Whisking-Related Changes in Neuronal Firing and Membrane Potential Dynamics in the Somatosensory Thalamus of Awake Mice

The thalamus transmits sensory information to the neocortex and receives neocortical, subcortical, and neuromodulatory inputs. Despite its obvious importance, surprisingly little is known about thalamic function in awake animals. Here, using intracellular and extracellular recordings in awake head-restrained mice, we investigate membrane potential dynamics and action potential firing in the two major thalamic nuclei related to whisker sensation, the ventral posterior medial nucleus (VPM) and the posterior medial group (Pom), which receive distinct inputs from brainstem and neocortex. We find heterogeneous state-dependent dynamics in both nuclei, with an overall increase in action potential firing during active states. Whisking increased putative lemniscal and corticothalamic excitatory inputs onto VPM and Pom neurons, respectively. A subpopulation of VPM cells fired spikes phase-locked to the whisking cycle during free whisking, and these cells may therefore signal whisker position. Our results suggest differential processing of whisking comparing thalamic nuclei at both sub- and supra-threshold levels.

Integrating petrography, mineralogy and hydrochemistry to constrain the influence and distribution of groundwater contributions to baseflow in poorly productive aquifers: insights from Gortinlieve catchment, Co. Donegal, NW Ireland

Identifying groundwater contributions to baseflow forms an essential part of surface water body characterisation. The Gortinlieve catchment (5 km(2)) comprises a headwater stream network of the Carrigans River, itself a tributary of the River Foyle, NW Ireland. The bedrock comprises poorly productive metasediments that are characterised by fracture porosity. We present the findings of a multi-disciplinary study that integrates new hydrochemical and mineralogical investigations with existing hydraulic, geophysical and structural data to identify the scales of groundwater flow and the nature of groundwater/bedrock interaction (chemical denudation). At the catchment scale, the development of deep weathering profiles is controlled by NE-SW regional scale fracture zones associated with mountain building during the Grampian orogeny. In-situ chemical denudation of mineral phases is controlled by micro- to meso-scale fractures related to Alpine compression during Palaeocene to Oligocene times. The alteration of primary muscovite, chlorite (clinochlore) and albite along the surfaces of these small-scale fractures has resulted in the precipitation of illite, montmorillonite and illite-montmorillonite clay admixtures. The interconnected but discontinuous nature of these small-scale structures highlights the role of larger scale faults and fissures in the supply and transportation of weathering solutions to/from the sites of mineral weathering. The dissolution of primarily mineral phases releases the major ions Mg, Ca and HCO3 that are shown to subsequently form the chemical makeup of groundwaters. Borehole groundwater and stream baseflow hydrochemical data are used to constrain the depths of groundwater flow pathways influencing the chemistry of surface waters throughout the stream profile. The results show that it is predominantly the lower part of the catchment, which receives inputs from catchment/regional scale groundwater flow, that is found to contribute to the maintenance of annual baseflow levels. This study identifies the importance of deep groundwater in maintaining annual baseflow levels in poorly productive bedrock systems.

A functional magnetic resonance imaging study of pathophysiological changes responsible for mirror movements in Parkinson's disease

Mirror movements correspond to involuntary movements observed in the limb contralateral to the one performing voluntary movement. They can be observed in Parkinson's disease (PD) but their pathophysiology remains unclear. The present study aims at identifying their neural correlates in PD using functional magnetic resonance imaging. Ten control subjects and 14-off drug patients with asymmetrical right-sided PD were included (8 with left-sided mirror movements during right-hand movements, and 6 without mirror movements). Between-group comparisons of BOLD signal were performed during right-hand movements and at rest (p<0.005 uncorrected). The comparison between PD patients with and without mirror movements showed that mirror movements were associated with an overactivation of the insula, precuneus/posterior cingulate cortex bilaterally and of the left inferior frontal cortex and with a deactivation of the right dorsolateral prefrontal cortex, medial prefrontal cortex, and pre-supplementary motor area and occipital cortex. These data suggest that mirror movements in Parkinson's disease are promoted by: 1- a deactivation of the non-mirroring inhibitory network (dorsolateral prefrontal cortex, pre-supplementary motor area); 2- an overactivation of prokinetic areas (notably the insula). The concomitant overactivation of a proactive inhibitory network (including the posterior cingulate cortex and precuneus) could reflect a compensatory inhibition of mirror movements.

Density and frequency caudo-rostral gradients of sleep spindles recorded in the human cortex

STUDY OBJECTIVE

This study aims at providing a quantitative description of intrinsic spindle frequency and density (number of spindles/min) in cortical areas using deep intracerebral recordings in humans.

PATIENTS OR PARTICIPANTS

Thirteen patients suffering from pharmaco-resistant focal epilepsy and investigated through deep intracortical EEG in frontal, parietal, temporal, occipital, insular, and limbic cortices including the hippocampus were included.

METHODS

Spindle waves were detected from the ongoing EEG during slow wave sleep (SWS) by performing a time-frequency analysis on filtered signals (band-pass filter: 10-16 Hz). Then, spindle intrinsic frequency was determined using a fast Fourier transform, and spindle density (number of spindles per minute) was computed.

RESULTS

Firstly, we showed that sleep spindles were recorded in all explored cortical areas, except temporal neocortex. In particular, we observed the presence of spindles during SWS in areas such as the insular cortex, medial parietal cortex, occipital cortex, and cingulate gyrus. Secondly, we demonstrated that both spindle frequency and density smoothly change along the caudo-rostral axis, from fast frequent posterior spindles to slower and less frequent anterior spindles. Thirdly, we identified the presence of spindle frequency oscillations in the hippocampus and the entorhinal cortex.

CONCLUSIONS

Spindling activity is widespread among cortical areas, which argues for the fundamental role of spindles in cortical functions. Mechanisms of caudo-rostral gradient modulation in spindle frequency and density may result from a complex interplay of intrinsic properties and extrinsic modulation of thalamocortical and corticothalamic neurons.

Implementation of an absolute brain 1H-MRS quantification method to assess different tissue alterations in multiple sclerosis

Magnetic resonance spectroscopy has emerged as a sensitive modality to detect early and diffuse alterations in multiple sclerosis. Recently, the hypothesis of neurodegenerative pathogenesis has highlightened the interest for measurement of metabolites concentrations, to gain specificity, in a large brain volume encompassing different tissue alterations. Therefore, we proposed in this paper the implementation of an absolute quantification method based on localized spectroscopy at short (30 ms) and long (135 ms) echo time of a volume including normal appearing white matter, cortical gray matter, and lesions. First, methodological developments were implemented including external calibration, and corrections of phased-array coil sensitivity and cerebrospinal fluid volume contribution. Second, these improvements were validated and optimized using an original methodology based on simulations of brain images with lesions. Finally, metabolic alterations were assessed in 65 patients including 26 relapsing-remitting, 17 primary-progressive (PP), 22 secondary-progressive (SP) patients, and in 23 normal subjects. Results showed increases of choline, creatine, and myo-inositol concentrations in PP and SP patients compared to controls, whereas the concentration of N-acetyl compounds remained constant. The major finding of this study was the identification of Cho concentration and Cho/tNA ratio as putative markers of progressive onset, suggesting interesting perspectives in detection and followup of neurodegenerative processes.

Paradoxical (REM) sleep deprivation causes a large and rapidly reversible decrease in long-term potentiation, synaptic transmission, glutamate receptor protein levels, and ERK/MAPK activation in the dorsal hippocampus

STUDY OBJECTIVES

It has been shown that wake (W) and slow wave sleep (SWS) modulate synaptic transmission in neocortical projections. However the impact of paradoxical sleep (PS) quantities on synaptic transmission remains unknown. We examined whether PS modulated the excitatory transmission and expression of glutamate receptor subtypes and phosphorylated extracellular signal-regulated kinases (p-ERK1/2).

DESIGN

PS deprivation (PSD) was carried out with the multiple platforms method on adult male Sprague-Dawley rats. LTP, late-LTP, and synaptic transmission were studied in the dorsal and ventral hippocampus of controls, 75-h PSD and 150-min PS rebound (PSR). GluR1 and NR1 protein and mRNA expression were evaluated by western blot and real-time PCR. p-ERK1/2 level was quantified by western blot and immunohistochemistry.

MEASUREMENT AND RESULTS

PSD decreased synaptic transmission and LTP selectively in dorsal CA1 and PSR rescued these deficits. PSD-induced synaptic modifications in CA1 were associated with a decrease in GluR1, NR1, and p-ERK1/2 levels in dorsal CA1 without change in GluR1 and NR1 mRNA expression. Regression analysis shows that LTP is positively correlated with both PS quantities and SWS episodes duration, whereas synaptic transmission and late-LTP are positively correlated with PS quantities and negatively correlated with SWS quantities.

CONCLUSIONS

These findings unveil previously unrecognized roles of PSD on synaptic transmission and LTP in the dorsal, but not in the ventral, hippocampus. The fact that the decrease in protein expression of GluR1 and NR1 was not associated with a change in mRNA expression of these receptors suggests that a sleep-induced modulation of translational mechanisms occurs in dorsal CA1.

Sleep dynamics: a self-organized critical system

In psychiatric and neurological diseases, sleep is often perturbed. Moreover, recent works on humans and animals tend to show that sleep plays a strong role in memory processes. Reciprocally, sleep dynamics following a learning task is modified [Hubert, Nature (London) 02663, 1 (2004), Peigneux, Neuron 44, 535 (2004)]. However, sleep analysis in humans and animals is often limited to the total sleep and wake duration quantification. These two parameters are not fully able to characterize the sleep dynamics. In mammals sleep presents a complex organization with an alternation of slow wave sleep (SWS) and paradoxical sleep (PS) episodes. Moreover, it has been shown recently that these sleep episodes are frequently interrupted by micro-arousal (without awakening). We present here a detailed analysis of the basal sleep properties emerging from the mechanisms underlying the vigilance states alternation in an animal model. These properties present a self-organized critical system signature and reveal the existence of two W, two SWS, and a PS structure exhibiting a criticality as met in sand piles. We propose a theoretical model of the sleep dynamics based on several interacting neuronal populations. This new model of sleep dynamics presents the same properties as experimentally observed, and explains the variability of the collected data. This experimental and theoretical study suggests that sleep dynamics shares several common features with critical systems.

Paradoxical sleep in mice lacking M3 and M2/M4 muscarinic receptors

Acetylcholine is crucial for the regulation of paradoxical sleep (PS) and EEG theta activity. To determine the contribution of individual muscarinic receptors to these events, we analyzed the sleep-waking cycle and EEG activities of mice lacking functional M(3) or M(2)/M(4 )receptors. Daily PS amounts were significantly decreased in M3-/- (-22%) but not in M2/M4-/- mice. Further, the theta peak frequency for PS was significantly increased in both M2/M4-/- and M3-/- mice. This study supports the potential role of M(3) rather than M(2) and M(4) muscarinic receptors in the modulation of PS in mice and strengthens the idea that multiple muscarinic receptors contribute to the regulation of the EEG theta activity during PS.

Exact discrete breather compactons in nonlinear Klein-Gordon lattices

We demonstrate the existence of exact discrete compact breather solutions in nonlinear Klein-Gordon systems, and complete the work of Tchofo Dinda and Remoissenet [Phys. Rev. E 60, 6218 (1999)], by showing that the breathers stability is related principally to the lattice boundary conditions, the coupling term, and the harmonicity parameter.

Exact discrete compactlike traveling kinks and pulses in phi(4) nonlinear lattices

We show that by properly choosing the analytical form of a solitary wave solution of discrete phi(4) models we can calculate the parameters of the potential which allow the propagation of compact (kink and pulses) solutions. Our numerical simulations show that narrow kinks and pulses with finite extent can propagate freely, and that discrete breathers with finite but long lifetime, can emerge from their collisions. Moreover, our numerical simulations reveal that the propagation of two successive pulses at a relative distance of two lattice spacings propagate freely, i.e., without interaction.

Discrete Burridge-Knopoff model, with exact solitonic or compactlike traveling wave solution

We have explored the dynamics of two versions of a Burridge-Knopoff model: with linear or nonlinear interactions between adjacent blocks. We have shown that by properly choosing the analytical form of the discrete solitary wave solution of the model we can calculate analytically the form of the friction function. In both cases our analytical results show that the friction force naturally presents the behavior of a simple weakening friction law first introduced qualitatively by Burridge and Knopoff [Bull. Seismol. Soc. Am. 57, 3411 (1967)] and quantitatively by Carlson and Langer [Phys. Rev. Lett. 62, 2632 (1989)]. With such a force function the discrete solitonic or compactlike wave-front solutions are exact and stable solutions. In the case of linear coupling our numerical simulations show that an irregular initial state evolves into kink pairs (large-amplitude events), that can recombine or not, plus nonlinear localized modes and small linear oscillations (small-amplitude events) that disperse with time, owing to dispersion. For nonlinear coupling one observes compactlike kink pairs or shocks, and a background of robust incoherent nonlinear oscillations (small amplitude events) that persist with time. Our results show that discreteness is a necessary ingredient to observe a rich and complex dynamical behavior. Nonlinearity allows the existence of strictly localized shocks.

Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments

Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.

Dissipative lattice model with exact traveling discrete kink-soliton solutions: discrete breather generation and reaction diffusion regime

We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.