arXiv subjects

Subhendu Chakraborty

Publications and source records attributed to Subhendu Chakraborty.

3 recordsLinked to original sources

arXiv2026

Neighbourhood second Zagreb matrix of graphs: spectral radius bounds and extremal graphs

Let $G$ be a connected graph on at least two vertices, and let $δ(i)$ be the sum of the degrees of the neighbours of a vertex $i$. The \emph{neighbourhood second Zagreb matrix} $\NF(G)$ has $(i,j)$-entry $δ(i)δ(j)$ if $i\sim j$ and $0$ otherwise; its spectral radius is denoted by $\rNF(G)$. We prove that $\rNF(G)\geρ(G)^{5}$, where $ρ(G)$ is the adjacency spectral radius, with equality if and only if $G$ is regular or bipartite semiregular, and we use this to show that the same graphs are exactly the extremal graphs of a Berman--Zhang--type upper bound. We sharpen the estimates $\demin^{2}ρ(G)\le\rNF(G)\le\demax^{2}ρ(G)$ by means of the extreme edge weights of $\NF(G)$, give sharp upper bounds in terms of the maximum degree $\dmax$, the maximum neighbourhood degree sum $\demax$, the size $m$ and the clique number $ω(G)$, and determine the extremal graphs for bipartite graphs and trees. For every connected unicyclic graph $G$ of order $n\ge3$ we prove $32=\rNF(C_n)\le\rNF(G)\le\rNF(\Sp n)$, where $\Sp n$ is the triangle with $n-3$ pendant edges at one vertex, with equality only for $C_n$ and only for $\Sp n$, respectively. Finally, we give bounds in terms of the first Zagreb index and for the neighbourhood second Zagreb energy; for lower energy bounds, the extremal graphs are described completely.

math.SP↗

arXiv2026

Strain-Rate- and Line-Length-Dependent Screw Dislocation Glide Mechanisms in BCC Refractory Metals and Alloys

Plastic flow in body-centered cubic (BCC) metals and dilute/concentrated alloys is governed by the motion of <111> screw dislocations, whose glide is often impeded by cross-kinks (jogs). While existing strengthening models typically treat depinning as defect-assisted cutting or dislocation bowing, the combined strain-rate and dislocation-line-length dependence of cross-kink stability and effective obstacle spacing remains insufficiently resolved at the atomistic scale. Here, we combine conventional molecular dynamics and strain-boost hyperdynamics to investigate screw-dislocation glide in pure Nb and Mo, dilute Nb-Mo alloys, and equiatomic NbMo at 300 K over strain rates from 10^3 to 10^7 s^-1 and dislocation line lengths from 15 to 50 nm. We first demonstrate that low-strain-rate simulations require sufficiently long dislocation lines to capture consistent cross-kink behavior and strength-determining pinning events. Using the 50~nm configurations, we show that cross-kinks form not only in concentrated alloys but also in pure BCC metals, with their stability governed by the relative rates of kink nucleation and migration on primary and cross-slip planes, which differ between Nb- and Mo-rich systems due to distinct core structures and non-Schmid responses. At high strain rates, depinning proceeds predominantly via vacancy-interstitial cluster formation. In contrast, at low strain rates and long line lengths, alternative pathways emerge, including lateral cross-kink migration, three-dimensional forward--backward cross-slip, and prismatic loop formation. The effective obstacle spacing controlling the critical resolved shear stress therefore emerges from coupled thermodynamic roughening and kinetic evolution. These findings highlight the intrinsically rate-, length-, and chemistry-dependent nature of screw-dislocation strengthening in BCC alloys.

cond-mat.mtrl-sci↗

arXiv2019

Destabilization, stabilization, and multiple attractors in saturated mixotrophic environments

The ability of mixotrophs to combine phototrophy and phagotrophy is now well recognized and found to have important implications for ecosystem dynamics. In this paper we examine the dynamical consequences of the invasion of mixotrophs in a model that is a limiting case of the chemostat. The model is a hybrid of a competition model describing the competition between populations of autotroph and mixotroph for limiting resources, and a predator-prey type model describing the interaction between populations of autotroph and herbivore. Our results show that mixotrophs are able to invade in both autotrophic environments and environments described by interactions between autotrophs and herbivores. The interaction between autotrophs and herbivores might be in equilibrium or cycle. We find that invading mixotrophs have the ability to both stabilize and destabilize autotroph-herbivore dynamics depending on the competitive ability of mixotrophs. Moreover the invasion of mixotrophs can also result in multiple attractors. Therefore, our results reveal important consequences of mixotrophic invasions in ecosystems depending on environmental conditions.

math.DS↗