The dual Derrida-Retaux conjecture

We consider a recursive system $(X_n)$ which was introduced by Collet et al. [10] as a spin glass model, and later by Derrida, Hakim, and Vannimenus [13] and by Derrida and Retaux [14] as a simplified hierarchical renormalization model. The system $(X_n)$ is expected to possess highly nontrivial universalities at or near criticality. In the nearly supercritical regime, Derrida and Retaux [14] conjectured that the free energy of the system decays exponentially with exponent $(p-p_c)^{-\frac12}$ as $p \downarrow p_c$. We study the nearly subcritical regime ($p \uparrow p_c$) and aim at a dual version of the Derrida-Retaux conjecture; our main result states that as $n \to \infty$, both \E(X_n) and $\P(X_n\neq 0)$ decay exponentially with exponent $(p_c-p)^{\frac12 +o(1)}$, where $o(1) \to 0$ as $p \uparrow p_c$

Synthesis of Na-Doped Lithium Metatitanate and Its Absorption for Carbon Dioxide

Na-doped lithium metatitanate (Na-doped Li2TiO3) absorbent was doped with Na2CO3 and lithium metatitanate (Li2TiO3) was prepared by a solid-state reaction method from mixture of TiO2 and Li2CO3. The Na-doped lithium metatitanate was characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) and surface area. Carbon dioxide absorption on Na-doped lithium metatitanate was investigated using TG-DTA. The results reveal an increase of the CO2 absorption capacity of the Na-doped materials with respect to pure Li2TiO3. XRD patterns of the doped samples suggest a limited substitution of Li by Na atoms within the Li2TiO3 structure. The results of experimental and modeling work were summarized to better understand the relationship between the sorbent microstructure and carbon dioxide absorption kinetics

The sustainability probability for the critical Derrida–Retaux model

International audienc

The dual Derrida--Retaux conjecture

We consider a recursive system $(X_n)$ which was introduced by Collet et al. [10] as a spin glass model, and later by Derrida, Hakim, and Vannimenus [13] and by Derrida and Retaux [14] as a simplified hierarchical renormalization model. The system $(X_n)$ is expected to possess highly nontrivial universalities at or near criticality. In the nearly supercritical regime, Derrida and Retaux [14] conjectured that the free energy of the system decays exponentially with exponent $(p-p_c)^{-\frac12}$ as $p \downarrow p_c$. We study the nearly subcritical regime ($p \uparrow p_c$) and aim at a dual version of the Derrida--Retaux conjecture; our main result states that as $n \to \infty$, both \E(X_n) and $\P(X_n\neq 0)$ decay exponentially with exponent $(p_c-p)^{\frac12 +o(1)}$, where $o(1) \to 0$ as $p \uparrow p_c$

The critical behaviors and the scaling functions of a coalescence equation

International audienceWe show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy model studied by Derrida and Retaux to mimic the depinning transition in presence of disorder. It was shown recently that this toy model exhibits the same critical behaviors as the equation studied in the present work. Here we find several families of exact solutions of this coalescence equation, in particular a family of scaling functions which are closely related to the different possible critical behaviors. These scaling functions lead to new conjectures, in particular on the shapes of the critical trees, that we have checked numerically

The New Graphene Family Materials: Synthesis and Applications in Oxygen Reduction Reaction

Graphene family materials, including graphene quantum dots (GQDs), graphene nanoribbons (GNRs) and 3D graphene (3D-G), have attracted much research interest for the oxygen reduction reaction (ORR) in fuel cells and metal-air batteries, due to their unique structural characteristics, such as abundant activate sites, edge effects and the interconnected network. In this review, we summarize recent developments in fabricating various new graphene family materials and their applications for use as ORR electrocatalysts. These new graphene family materials play an important role in improving the ORR performance, thus promoting the practical use in metal-air batteries and fuel cells

A hierarchical renormalization model: some properties and open questions

We consider a simple hierarchical renormalization model which was introduced in the study of depinning transition in presence of strong disorder, by Derrida and Retaux. Our interest is focused on the critical regime, for which we study the extinction probability, the first moment and the moment generating function. Several stronger assertions are stated as conjectures

Hyperhomocysteinemia is a result, rather than a cause, of depression under chronic stress.

BACKGROUND: Although the accumulation of homocysteine (Hcy) has been implicated in the pathogenesis of depression, whether Hcy is directly involved and acts as the primary cause of depressive symptoms remains unclear. The present study was designed to clarify whether increased Hcy plays an important role in stress-induced depression. RESULTS: We employed the chronic unpredictable mild stress model (CUMS) of depression for 8 weeks to observe changes in the plasma Hcy level in the development of depression. The results showed that Wistar rats exposed to a series of mild, unpredictable stressors for 4 weeks displayed depression-like symptoms such as anhedonia (decreased sucrose preferences) and a decreased 5-Hydroxy Tryptophan (5-HT) concentration in the hippocampus. At the end of 8 weeks, the plasma Hcy level increased in the CUMS rats. The anti-depressant sertraline could decrease the plasma Hcy level and improve the depression-like symptoms in the CUMS rats. RhBHMT, an Hcy metabolic enzyme, could decrease the plasma Hcy level significantly, although it could not improve the depressive symptoms in the CUMS rats. CONCLUSIONS: The results obtained from the experiments did not support the hypothesis that the increased Hcy concentration mediated the provocation of depression in CUMS rats, and the findings suggested that the increased Hcy concentration in the plasma might be the result of stress-induced depression

The Derrida--Retaux conjecture on recursive models

We are interested in the nearly supercritical regime in a family of max-type recursive models studied by Derrida and Retaux, and prove that under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent $\tfrac12$. This gives a weaker answer to a conjecture of Derrida and Retaux. Other behaviours are obtained when the integrability condition is not satisfied