Mathematical modeling of the Chilean riots of 2019: An epidemiological non-local approach

During the second half of October 2019, Chile, especially the capital city, Santiago, suffered from widespread violence and public and private infrastructure destruction. This work aims to expand an epidemiological non-local model that successfully described the French riots of 2005 to incorporate the topology of Santiago's subway network and explain the reported distribution of rioting activity in the city. Although the model reproduced the disorders' aggregated temporal evolution, it could not deliver results resembling the observed spatial distribution of activity on Santiago. The main reason for this failure can be attributed to the fact that the model lacks a population displacement mechanism, which seems vital to explain Santiago's unrest episodes.

Riots and subways, a relationship moderated by the neighborhood's income level

Social disturbances due to socioeconomic and political factors received media attention during 2019 in places like France, Hong Kong, Chile, Nigeria, Sudan, Haiti, and Lebanon. In October 2019, Chile saw massive demonstrations in the capital city of Santiago. The cost of damage to infrastructure during the first month of unrest was estimated at US$ 4.6 billion, and the cost to the Chilean economy was about US$ 3 billion, 1.1% of its Gross Domestic Product. This study analyzes how the topology of the public transport network affected the locations of the 2019 riots in Santiago. On average, we find a clear association between proximity to the subway network and riot density. This association is significant only in neighborhoods with residents in the highest and lowest income quartiles. As a result, when analyzing social unrest and the critical role of public transport, policymakers should also consider the crucial role of income.

Oscillatory dissipative solitons stabilized by nonlinear gradient terms: The transition to localized spatiotemporal disorder

We investigate properties of oscillatory dissipative solitons (DSs) in a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. As a main result we find a transition to dissipative solitons with spatiotemporal disorder as a function of the diffusion coefficient. This transition proceeds via quasiperiodicity and shows incommensurate satellites next to the fundamental frequency and its harmonics indicating a possible route to localized spatiotemporal chaos. The transition back to oscillatory DSs follows a similar scenario.

The Galerkin-truncated Burgers equation: crossover from inviscid-thermalized to Kardar-Parisi-Zhang scaling

The one-dimensional Galerkin-truncated Burgers equation, with both dissipation and noise terms included, is studied using spectral methods. When the truncation-scale Reynolds number [Formula: see text] is varied, from very small values to order 1 values, the scale-dependent correlation time [Formula: see text] is shown to follow the expected crossover from the short-distance [Formula: see text] Edwards-Wilkinson scaling to the universal long-distance Kardar-Parisi-Zhang scaling [Formula: see text]. In the inviscid limit, [Formula: see text], we show that the system displays another crossover to the Galerkin-truncated inviscid-Burgers regime that admits thermalized solutions with [Formula: see text]. The scaling forms of the time-correlation functions are shown to follow the known analytical laws and the skewness and excess kurtosis of the interface increments distributions are characterized. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Transcriptional analysis of metabolic and virulence genes associated with biofilm formation in Piscirickettsia salmonis strains

Piscirickettsia salmonis is a facultative intracellular bacterium that generates piscirickettsiosis affecting salmonids in Chile. The bacterium has the adaptability to survive in the marine environment under multiple stressful conditions. In this sense, this work focused on the analysis of a gene battery associated with biofilm formation under different culture conditions and on the adaptability of this biofilm to different media. The results indicated that the strains LF-89, IBM-034 and IBM-040 were strong biofilm producers, evidencing adaptability to the media by increasing the amount of biofilm through successive growths. Transcript levels of six genes described in various bacteria and P. salmonis, considered to have metabolic functions, and playing a relevant role in biofilm formation, were analyzed to evaluate bacterial functionality in the biofilm. The genes mazE-mazF, implicated in biofilm and stress, were markedly overexpressed in the biofilm condition in the three strains. For its part, gene gltA, an indicator of metabolic activity and related to virulence inhibition in Salmonella typhimurium, also seems to restrain the pathogenesis process in P. salmonis by inhibiting the expression of the virulence-associated genes liso and tcf. Finally, the expression of the glnA gene suggests the use of glutamine as an essential element for the growth of the biofilm.

Multiplicative noise can induce a velocity change of propagating dissipative solitons

We investigate the influence of spatially homogeneous multiplicative noise on propagating dissipative solitons (DSs) of the cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. Here we focus on the nonlinear gradient terms, in particular on the influence of the Raman term and the delayed nonlinear gain. We show that a fairly small amount of multiplicative noise can lead to a change in the mean velocity for such systems. This effect is exclusively due to the presence of the stabilizing nonlinear gradient terms. For a range of parameters we find a velocity change proportional to the noise intensity for the Raman term and for delayed nonlinear gain. We note that the dissipative soliton decreases the modulus of its velocity when only one type of nonlinear gradient is present. We present a straightforward mean field analysis to capture this simple scaling law. At sufficiently high noise strength the nonlinear gradient stabilized DSs collapse.

Analysis of genes encoding for proteolytic enzymes and cytotoxic proteins as virulence factors of Piscirickettsia salmonis in SHK-1 cells

Piscirickettsia salmonis is the causative agent of Piscirickettsiosis, a systemic disease generating high mortality rates in farmed salmon cultures of southern Chile. Proteolytic enzymes are important virulence factors since they play a key role in bacterial invasion and proliferation within the host. Bacteria growing in muscle tissues are known to secrete proteases, but no proteolytic enzymes have been described in P. salmonis to date. A battery of putative protease genes was found in the genomes and available strains of P. salmonis by bioinformatics analyses, and their identity was established through comparison with protease genes in databases. The transcript levels of five candidate genes were analysed by in vitro infection and qPCR. All strains were found to generate protease activity to varying degrees, and this was significantly increased when bacteria infected a salmon cell line. Gene expression of several types of proteases was also evidenced, with the highest levels corresponding to the type 1 secretion system (T1SS), which is also involved in the transport of haemolysin A, although transcripts with significant levels of peptidase M4 (thermolysin) and CLP protease were also found.

Interaction of dissipative solitons stabilized by nonlinear gradient terms

We study the interaction of stable dissipative solitons of the cubic complex Ginzburg-Landau equation which are stabilized only by nonlinear gradient terms. In this paper we focus for the interactions in particular on the influence of the nonlinear gradient term associated with the Raman effect. Depending on its magnitude, we find up to seven possible outcomes of theses collisions: Stationary bound states, oscillatory bound states, meandering oscillatory bound states, bound states with large-amplitude oscillations, partial annihilation, complete annihilation, and interpenetration. Detailed results and their analysis are presented for one value of the corresponding nonlinear gradient term, while the results for two other values are just mentioned briefly. We compare our results with those obtained for coupled cubic-quintic complex Ginzburg-Landau equations and with the cubic-quintic complex Swift-Hohenberg equation. It turns out that both meandering oscillatory bound states as well as bound states with large-amplitude oscillations appear to be specific for coupled cubic complex Ginzburg-Landau equations with a stabilizing cubic nonlinear gradient term. Remarkably, we find for the large-amplitude oscillations a linear relationship between oscillation amplitude and period.

The anatomy of the 2019 Chilean social unrest

We analyze the 2019 Chilean social unrest episode, consisting of a sequence of events, through the lens of an epidemic-like model that considers global contagious dynamics. We adjust the parameters to the Chilean social unrest aggregated public data available from the Undersecretary of Human Rights and observe that the number of violent events follows a well-defined pattern already observed in various public disorder episodes in other countries since the 1960s. Although the epidemic-like models display a single event that reaches a peak followed by an exponential decay, we add standard perturbation schemes that may produce a rich temporal behavior as observed in the 2019 Chilean social turmoil. Although we only have access to aggregated data, we are still able to fit it to our model quite well, providing interesting insights on social unrest dynamics.

Random walks of trains of dissipative solitons

The propagation of light pulses in dual-core nonlinear optical fibers is studied using a model proposed by Sakaguchi and Malomed. The system consists of a supercritical complex Ginzburg-Landau equation coupled to a linear equation. Our analysis includes single standing and walking solitons as well as walking trains of 3, 5, 6, and 12 solitons. For the characterization of the different scenarios, we used ensemble-averaged square displacement of the soliton trajectories and time-averaged power spectrum of the background waves. Power law spectra, indicative of turbulence, were found to be associated with random walks. The number of solitons (or their separations) can trigger anomalous random walks or totally suppress the background waves.

Analysis of single nucleotide polymorphisms (SNPs) associated with antibiotic resistance genes in Chilean Piscirickettsia salmonis strains

The aetiological agent of Piscirickettsiosis is Piscirickettsia salmonis, a Gram-negative intracellular pathogen, and high doses of antibiotics have regularly been employed to treat this infection. Seven florfenicol and/or oxytetracycline resistance genes (tet pump, tetE, Tclor/flor, Tbcr, TfloR, ompF and mdtN) were identified in strains by in silico genome analyses. Later, the number of single nucleotide polymorphisms (SNPs) and its relationship with the resistance to these antibiotics were identified and analysed, using the original LF-89 strain as reference. Trials to determine and compare the minimum inhibitory concentration (MIC) of oxytetracycline and florfenicol in each strain, as well as to quantify the gPCR transcripts levels in the selected genes, were performed. Therefore, variations in the resistance to both antibiotics were observed, where the strain with fewer SNPs showed the highest susceptibility. Consistently, the in silico 3D analyses of proteins encoded by the selected genes revealed structural changes, evident in the sequences with the highest number of SNPs. These results showed that the bacterial resistance to oxytetracycline was mainly linked to the presence of SNPs in relevant sites, antibiotic resistance genes and an OmpF porin, leading to important changes in the protein structure.

Dry eye is matched by increased intrasubject variability in tear osmolarity as confirmed by machine learning approach

OBJECTIVE

Because of high variability, tear film osmolarity measures have been questioned in dry eye assessment. Understanding the origin of such variability would aid data interpretation. This study aims to evaluate osmolarity variability in a clinical setting.

MATERIAL AND METHODS

Twenty dry eyes and 20 control patients were evaluated. Three consecutive osmolarity measurements per eye at 5min intervals were obtained. Variability was represented by the difference between both extreme readings per eye. Machine learning techniques were used to quantify discrimination capacity of tear osmolarity for dry eye.

RESULTS

Mean osmolarities in the control and dry eye groups were 295.1±7.3mOsm/L and 300.6±11.2mOsm/L, respectively (P=.004). Osmolarity variabilities were 7.5±3.6mOsm/L and 16.7±11.9mOsm/L, for the control and dry eye groups, respectively (P<.001). Based on osmolarity, a logistic classifier showed an 85% classification accuracy.

CONCLUSIONS

In the clinical setting, both mean osmolarity and osmolarity variability in the dry eye group were significantly higher than in the control group. Machine learning techniques showed good classification accuracy. It is concluded that higher variability of tear osmolarity is a dry eye feature.

Simultaneous influence of additive and multiplicative noise on stationary dissipative solitons

We investigate the simultaneous influence of spatially homogeneous multiplicative noise as well as of spatially δ-correlated additive noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. Depending on the ratio between the strength of additive and multiplicative noise we find a number of distinctly different types of behavior including explosions, collapse, filling in, and spatio-temporal disorder as well as intermittent behavior of all types listed. Techniques used to analyze the results include snapshots, x-t plots and plots of the spatially and temporally averaged amplitude as a function of the strength of multiplicative noise while keeping the strength of additive noise fixed. Typically 50 realizations are used for averaging to obtain the corresponding data points in these diagrams. For the widths of these distribution as a function of additive noise we obtain a linear decrease in the limit of fairly large, but fixed values of the multiplicative noise. To summarize our findings concisely we show three-dimensional plots of the mean pattern amplitude and the generalized susceptibility as a function of the strengths of additive and multiplicative noise. We critically compare the results of our investigations with those obtained in the two limiting cases of purely additive and of purely multiplicative noise.

Ahmed glaucoma drainage implant surgery in the management of refractory uveitic glaucoma: Long-term follow up

OBJECTIVE

To examine the long-term efficacy, safety and complications of Ahmed glaucoma drainage implant surgery in patients with refractory uveitic glaucoma.

METHODS

Retrospective review of consecutive cases of patients with refractory uveitic glaucoma who underwent Ahmed glaucoma drainage implant surgery between 2004-2014. Demographic characteristics of the study population, visual acuity, intraocular pressure (IOP), number of antiglaucoma medications and operative and postoperative complications were recorded. Complete success was defined as IOP≥5 and ≤18mmHg without any medication, as qualified success if IOP≤18mmHg with one or more medications. Patients with less than 12 months of follow-up were excluded.

RESULTS

21 patients (26 eyes) were included. The mean postoperative follow-up was 53.5±31 months. Eight eyes (30%) had at least one previously failed glaucoma surgery. IOP was reduced from a mean of 30.0mmHg to 14.0mmHg at the last follow-up visit (P<.001). The number of IOP-lowering medications was reduced from a median of 2.9 preoperatively to 1.1 at the last follow-up (P<.001). Overall, 7 eyes (27%) were classified as complete success, 13 eyes (50%) were considered as qualified success, and 6 eyes (23%) met the criteria for failure. The most common postoperative complication was hypertensive phase in 12 eyes (46%). Kaplan-Meier life-table analysis showed a cumulative probability of success after Ahmed glaucoma valve implantation of 65% at 84 months.

CONCLUSIONS

Ahmed glaucoma drainage implant surgery may be considered a long-term effective and safety surgical option for patients with refractory uveitic glaucoma.

Identification of genomic islands in Chilean Piscirickettsia salmonis strains and analysis of gene expression involved in virulence

Piscirickettsia salmonis, an agent of Piscirickettsiosis, is the cause of major losses in the Chilean salmon industry. We identified, characterized and bioinformatically analysed genomic islands in field strains of P. Salmonis, using the bioinformatic software PIPS, that uses the characteristics of the islands of pathogenicity to identify them. We analysed nine partially sequenced genomes in different new field strains, and compared them with the LF-89 (Type strain) genome, selecting a genomic island present in all of them. We then evaluated the relative expression of three genes present in that island. From the obtained results, we conclude that the expression of the tcf gene is directly proportional to the cytopathogenicity in vitro of the bacteria; the product of the dnsa gene could contribute to its pathogenicity, but would be potentiated by one or more factors. The product of the gene liso is necessary for the virulence process and could have functions in early stages of infection. Regarding the strains, the IBM-040 strain showed a significant increase in the expression of all the genes in the study. Contrarily, LF-89 only presented a significant increase in expression of the gene liso, which correlates with the cytopathogenicity in vitro observed in the SHK-1 cells.

Search and analysis of genes involved in antibiotic resistance in Chilean strains of Piscirickettsia salmonis

Piscirickettsia salmonis is the pathogen causing Piscirickettsiosis. For treatment, the industry mainly uses oxytetracycline and florfenicol, so it is essential to understand the degree of susceptibility of this pathogen to these drugs. But this is still unknown for a large number of P. salmonis strains, as are the molecular mechanisms responsible for greater or lesser susceptibility. However, genes that confer resistance to these antimicrobials have been reported and characterized for this and other bacterial species, among which are membrane proteins that take out the drug. Our results identified differences in the degree of susceptibility to both antibiotics among different Chilean isolated of these bacteria. We analysed 10 available genomes in our laboratory and identified ~140 genes likely to be involved in antibiotic resistance. We analysed six specific genes, which suggests that some of them would eventually be relevant in conferring resistance to both antibiotics, as they encode for specific transporter proteins, which increase the number of transcripts when grown in media with these antibiotics. Our results were corroborated with EtBr permeability analysis, which revealed that the LF-89 strain accumulates this compound and has a reduced capacity to expulse it compared with the field strains.

High prevalence of Demodex spp. infestation among patients with posterior blepharitis: correlation with age and cylindrical dandruff

OBJECTIVE

To determine prevalence of Demodex spp. and infestation index (II) by the parasite among patients of different ages with blepharitis and to assess association with occurrence of cylindrical dandruff (CC).

MATERIALS AND METHODS

Prospective study including patients diagnosed with posterior blepharitis between 2013 and 2015, without previous acaricide treatment, was conducted by Fundación Oftalmológica Los Andes (Chile). Four eyelashes were randomly extracted from each eyelid for parasite detection. The II was calculated as the ratio between the total number of demodex specimens found in the total number of eyelashes removed. A semi-quantitative determination of the CC was performed.

RESULTS

A total of 178 patients (91 men, 87 women), with a mean age of 58.49±20.66 years, were included. It was found that 83.7% of patients were infested with Demodex folliculorum with a mean II of 0.96±0.84 mites/eyelash. The II was significantly higher in patients over 50 years (p<.0001). Patient age and II showed a Pearson correlation coefficient (R²) of 0.12 (p<.0001). CC was observed in 71.4% of patients, with those over 50 years-old showing significantly higher values. A positive correlation was also observed between the amount of CC and the II (R²=.33; p<.0001).

CONCLUSIONS

The prevalence of infestation by Demodex folliculorum is high in patients with posterior blepharitis. The II by the parasite is positively correlated with age and with the occurrence of CC on the eyelid border.

On the influence of additive and multiplicative noise on holes in dissipative systems

We investigate the influence of noise on deterministically stable holes in the cubic-quintic complex Ginzburg-Landau equation. Inspired by experimental possibilities, we specifically study two types of noise: additive noise delta-correlated in space and spatially homogeneous multiplicative noise on the formation of π-holes and 2π-holes. Our results include the following main features. For large enough additive noise, we always find a transition to the noisy version of the spatially homogeneous finite amplitude solution, while for sufficiently large multiplicative noise, a collapse occurs to the zero amplitude solution. The latter type of behavior, while unexpected deterministically, can be traced back to a characteristic feature of multiplicative noise; the zero solution acts as the analogue of an absorbing boundary: once trapped at zero, the system cannot escape. For 2π-holes, which exist deterministically over a fairly small range of values of subcriticality, one can induce a transition to a π-hole (for additive noise) or to a noise-sustained pulse (for multiplicative noise). This observation opens the possibility of noise-induced switching back and forth from and to 2π-holes.

Multiplicative noise can lead to the collapse of dissipative solitons

We investigate the influence of spatially homogeneous multiplicative noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. We find that for sufficiently large multiplicative noise the formation of stationary and temporally periodic dissipative solitons is suppressed. This result is characterized by a linear relation between the bifurcation parameter and the noise amplitude required for suppression. For the regime associated with exploding dissipative solitons we find a reduction in the number of explosions for larger noise strength as well as a conversion to other types of dissipative solitons or to filling-in and eventually a collapse to the zero solution.

Transition from non-periodic to periodic explosions

We show the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order nonlinear and dispersive effects are added to the complex cubic-quintic Ginzburg-Landau equation modelling soliton transmission lines. This counterintuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations (or intermittency) leading to chaos (non-periodic explosions).

Noisy localized structures induced by large noise

We investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular, subcriticality, for which stationary stable deterministic pulses do not exist. Possible experimental tests of the work presented for autocatalytic chemical reactions and bioinspired systems are outlined.

[Telemedicine correlation in retinopathy of prematurity between experts and non-expert observers]

OBJECTIVE

To study the correlation between expert and non-expert observers in the reporting images for the diagnosis of retinopathy of prematurity (ROP) in a telemedicine setting.

METHODS

A cross-sectional, multicenter study, consisting of 25 sets of images of patients screened for ROP. They were evaluated by two experts in ROP and 1 non-expert and classified according to telemedicine classification, zone, stage, plus disease and Ells referral criteria. The telemedicine classification was: no ROP, mild ROP, type 2 ROP, or ROP that requires treatment. Ells referral criteria is defined as the presence at least one of the following: ROP in zone I, Stage 3 in zone I or II, or plus+ For statistical analysis, SPSS 16.0 was used. For correlation, Kappa value was performed.

RESULTS

There was a high correlation between observers for the assessment of ROP stage (0.75; 0.54-0.88) plus disease (0.85; 0.71-0.92), and Ells criteria (0.89; 0.83-1.0). However, inter-observer values were low for zone (0.41; 0.27-0.54) and telemedicine classification (0.43; 0.33-0.6).

CONCLUSIONS

When evaluating telemedicine images by examiners with different levels of expertise in ROP, the Ells criteria gave the best correlation. In addition, stage of disease and plus disease have good correlation among observers. In contrast, the correlation between observers was low for zone and telemedicine classification.

Model of a two-dimensional extended chaotic system: evidence of diffusing dissipative solitons

We investigate a two-dimensional extended system showing chaotic and localized structures. We demonstrate the robust and stable existence of two types of exploding dissipative solitons. We show that the center of mass of asymmetric dissipative solitons undergoes a random walk despite the deterministic character of the underlying model. Since dissipative solitons are stable in two-dimensional systems we conjecture that our predictions can be tested in systems as diverse as nonlinear optics, parametric excitation of granular media and clay suspensions, and sheared electroconvection.

Noise can induce explosions for dissipative solitons

We study the influence of noise on the spatially localized, temporally regular states (stationary, one frequency, two frequencies) in the regime of anomalous dispersion for the cubic-quintic complex Ginzburg-Landau equation as a function of the bifurcation parameter. We find that noise of a fairly small strength η is sufficient to reach a chaotic state with exploding dissipative solitons. That means that noise can induce explosions over a fairly large range of values of the bifurcation parameter μ. Three different routes to chaos with exploding dissipative solitons are found as a function of μ. As diagnostic tools we use the separation to characterize chaotic behavior and the energy to detect spatially localized explosive behavior as a function of time.

Exploding dissipative solitons: the analog of the Ruelle-Takens route for spatially localized solutions

We investigate the route to exploding dissipative solitons in the complex cubic-quintic Ginzburg-Landau equation, as the bifurcation parameter, the distance from linear onset, is increased. We find for a large class of initial conditions the sequence: stationary localized solutions, oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding localized solutions. The transition between localized solutions with one and with two frequencies, respectively, is analyzed in detail. It is found to correspond to a forward Hopf bifurcation for these localized solutions as the bifurcation parameter is increased. In addition, we make use of power spectra to characterize all time-dependent states. On the basis of all information available, we conclude that the sequence oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding dissipative solitons can be interpreted as the analog of the Ruelle-Takens-Newhouse route to chaos for spatially localized solutions.

Presumed consent for organ donation: is Romania prepared for it?

INTRODUCTION

In November 2007, a legislative initiative regarding the presumed consent for organ donation was proposed for parliamentary debate in Romania and was followed by public debate. The study aimed to asses public opinions expressed in the Romanian media.

MATERIALS AND METHODS

An Internet search was made. The pro and con reasons, the affiliation of parts involved in the debate and suggested future direction of action were identified.

RESULTS

The Internet search had 8572 results. The parts involved in the pro and con debate consisted of governmental structures, physicians, ethicists, politicians, media, religious authorities, nongovernmental associations, and lay persons. The main pros were the low rate of organ donation and the long waiting lists, enhancement of organ procurement, avoidance of wasting valuable organs, avoiding responsibility, and the stress imposed to the family in giving the donation consent, humanitarian purposes (saving lives), going along with the scientific progress, and less bureaucracy. The main cons were an unethical issue, violation of human rights, denial of brain death, unethical advantage of public ignorance, unethical use of underprivileged people, little results in terms of organ procurement, but huge negative effects on public opinion, public mistrust in transplant programs and impossibility of refusal identification due to particularities of the Romanian medical system.

CONCLUSION

The con opinions prevailed. For the moment, Romania seems to be unprepared to accept presumed consent. A future change in public perception regarding organ transplantation may modify the terms of a public debate.

van der Waals normal form for a one-dimensional hydrodynamic model

Phase separation in a fluidized granular system is studied. We consider a one-dimensional hydrodynamic model that mimics a two-dimensional fluidized granular system with a vibrating wall and without gravity, which exhibits a phase separation. Close to the critical point, by means of an adiabatic elimination of the temperature, we deduce the van der Waals normal form, which is the equation that describes the slow dynamics of the system and predicts the qualitative behavior in different regions of parameters. This allows us to understand the origin of the effective viscosity and the spatial saturation at the onset of the bifurcation. The hydrodynamic model and van der Waals normal form exhibit a behavior similar to the one observed in molecular dynamics simulations.