arXiv subjects

Krishnendu Paul

Publications and source records attributed to Krishnendu Paul.

11 recordsLinked to original sources

arXiv2026

Frictional timescales and the impact of climate change-driven extreme weather on rainfall-triggered landslides in Mizoram, NE India

Mizoram records the highest landslide frequency among all Indian states, yet physics-based models that predict the timing of slope failure remain unavailable for the region. Here, we apply the rate-and-state friction (RSF) block-slider framework of Paul et al.(2024) to 19 rainfall-triggered landslides in and around Aizawl (2016--2025) to investigate the hydro-mechanical coupling between pore-pressure transients and the slow-to-fast transition of slopes hosted in Miocene shale-dominated lithology. For each event, satellite-derived (GPM) rainfall is propagated to failure depth using a 1D infiltration model across three hydraulic conductivity scenarios, and RSF parameters are inverted to reproduce the observed failure date. The resulting dimensionless normalized pore-pressure $\chi = \mu_0 \Delta P / (a\,\sigma'_f)$ cleanly separates the 19 events into two dynamically distinct failure regimes: synchronous failure ($\chi \gtrsim 4$, zero delay from peak pore-pressure), exemplified by the eight-event Cyclone Remal cluster of May 2024, and delayed failure ($\chi \sim 1$--$3$, delays of hours to 10~days), controlled jointly by $\chi$ and the velocity-weakening ratio $a/b$. Using CMIP6 extreme-rainfall scaling factors for northeast India under SSP2-4.5, SSP3-7.0 and SSP5-8.5 scenarios, we project that the fraction of landslides falling in the zero-warning synchronous regime increases from the current $\sim$56% to $\sim$72% under SSP5-8.5. Our results imply a significant climate-driven escalation of multi-site, clustered landslide failure risk driven by the intensification of extreme precipitation events.

physics.geo-ph↗

arXiv2026

$\{\pm 1\}$-weighted zero-sum constants

Let $A,B\subseteq \mathbb Z_n\setminus\{0\}$. A sequence $S=(x_1,\ldots, x_k)$ in $\mathbb Z_n$ is called an $(A,B)$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in A$ and $b_1,\ldots,b_k\in B$ such that $a_1x_1+\cdots+a_kx_k=0$ and $b_1a_1+\cdots+b_ka_k=0$. The constant $E_{A,B}(n)$ is defined to be the smallest positive integer $k$ such that every sequence of length $k$ in $\mathbb Z_n$ has an $(A,B)$-weighted zero-sum subsequence of length $n$. We determine the constant $E_{A,B}(n)$ and the related constants $C_{A,B}(n)$ and $D_{A,B}(n)$ when $A=\{\pm 1\}$ and $B=\{1\}$.

math.NT↗

arXiv2026

$Q_p$-weighted zero-sum constants

A sequence $S=(x_1,\ldots, x_k)$ in $\mathbb Z_p$ is called a $(Q_p,\mathbf 1)$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in Q_p$ such that $a_1x_1+\cdots+a_kx_k=0$ and $a_1+\cdots+a_k=0$. The constant $E_{Q_p,\mathbf 1}$ is defined to be the smallest positive integer $k$ such that every sequence of length $k$ in $\mathbb Z_p$ has a $(Q_p,\mathbf 1)$-weighted zero-sum subsequence of length $p$. We determine the constant $E_{Q_p,\mathbf 1}$ and the related constants $C_{Q_p,\mathbf 1}$ and $D_{Q_p,\mathbf 1}$. We also study some $(Q_p,B)$-weighted zero-sum constants where $B$ is a subset of $Q_p$.

math.NT↗

arXiv2024

Square-weighted zero-sum constants

Let $A\subseteq \mathbb Z_n$ be a subset. A sequence $S=(x_1,\ldots,x_k)$ in $\mathbb Z_n$ is said to be an $A$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in A$ such that $a_1x_1+\cdots+a_kx_k=0$. By a square, we shall mean a non-zero square in $\mathbb Z_n$. We determine the smallest natural number $k$, such that every sequence in $\mathbb Z_n$ whose length is $k$, has a square-weighted zero-sum subsequence. We also determine the smallest natural number $k$, such that every sequence in $\mathbb Z_n$ whose length is $k$, has a square-weighted zero-sum subsequence whose terms are consecutive terms of the given sequence.

math.NT↗

arXiv2023

Doubly-weighted zero-sum constants

Let $A,B\subseteq\mathbb Z_n$ be given and $S=(x_1,\ldots, x_k)$ be a sequence in $\mathbb Z_n$. We say that $S$ is an $(A,B)$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in A$ and $b_1,\ldots,b_k\in B$ such that $a_1x_1+\cdots+a_kx_k=0$ and $b_1a_1+\cdots+b_ka_k=0$. We show that if $S$ has length $2n-1$, then $S$ has an $(A,B)$-weighted zero-sum subsequence of length $n$. The constant $E_{A,B}$ is defined to be the smallest positive integer $k$ such that every sequence of length $k$ in $\mathbb Z_n$ has an $(A,B)$-weighted zero-sum subsequence of length $n$. A sequence in $\mathbb Z_n$ of length $E_{A,B}-1$ which does not have any $(A,B)$-weighted zero-sum subsequence of length $n$ is called an $E$-extremal sequence for $(A,B)$. We determine the constant $E_{A,B}$ and characterize the $E$-extremal sequences for some pairs $(A,B)$. We also study the related constants $C_{A,B}$ and $D_{A,B}$ which are defined in the article.

math.NT↗

arXiv2023

On unit-weighted zero-sum constants of $\mathbb Z_n$

Given $A\subseteq\mathbb Z_n$, the constant $C_A(n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $\mathbb Z_n$ has an $A$-weighted zero-sum subsequence having consecutive terms. The value of $C_{U(n)}(n)$ is known when $n$ is odd. We give a different argument to determine the value of $C_{U(n)}(n)$ for any $n$. A $C$-extremal sequence for $U(n)$ is a sequence in $\mathbb Z_n$ whose length is $C_{U(n)}(n)-1$ and which does not have any $U(n)$-weighted zero-sum subsequence having consecutive terms. We characterize the $C$-extremal sequences for $U(n)$ when $n$ is a power of 2. For any $n$, we determine the value of $C_A(n)$ where $A$ is the set of all odd (or all even) elements of $\mathbb Z_n$ and also when $A=\{1,2,\ldots,r\}$ where $r<n$.

math.NT↗

arXiv2023

Zero-sum constants related to the Jacobi symbol

For $A\subseteq\mathbb Z_n$, the $A$-weighted Gao constant $E_A(n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $\mathbb Z_n$ has a subsequence of length $n$ whose $A$-weighted sum is zero. When $A$ is the set of all units in $\mathbb Z_n$, we determine the value of $E_A(n)$ and values of two related constants $C_A(n)$ and $D_A(n)$. We also characterize all sequences of length $E_A(n)-1$ in $\mathbb Z_n$ which do not have any $A$-weighted zero-sum subsequence of length $n$ when $n$ is a power of 2.

math.NT↗

arXiv2023

On a different weighted zero-sum constant

For a finite abelian group $(G,+)$, the constant $C(G)$ is defined to be the smallest natural number $k$ such that any sequence in $G$ having length $k$ will have a subsequence of consecutive terms whose sum is zero. For a subset $A\subseteq\mathbb Z_n$, the constant $C_A(n)$ is the smallest natural number $k$ such that any sequence in $G$ having length $k$ has an $A$-weighted zero-sum subsequence of consecutive terms. We determine the value of $C_A(n)$ for some particular weight-sets $A$.

math.NT↗

arXiv2022

Extremal sequences related to the Jacobi symbol

For a weight-set $A\subseteq \mathbb Z_n$, the $A$-weighted zero-sum constant $C_A(n)$ is defined to be the smallest natural number $k$, such that any sequence of $k$ elements in $\mathbb Z_n$ has an $A$-weighted zero-sum subsequence of consecutive terms. A sequence of length $C_A(n)-1$ in $\mathbb Z_n$ which does not have any $A$-weighted zero-sum subsequence of consecutive terms will be called a $C$-extremal sequence for $A$. Let $\big(\frac{x}{n}\big)$ denote the Jacobi symbol of $x\in\mathbb Z_n$. We characterize the $C$-extremal sequences for the weight-set $S(n)=\big\{\,x\in U(n):\big(\frac{x}{n}\big)=1\,\big\}$ and for the weight-set $L(n;p)=\big\{\,x\in U(n):\big(\frac{x}{n}\big)=\big(\frac{x}{p}\big)\,\big\}$ where $p$ is a prime divisor of $n$. We can define $D$-extremal sequences for these weight-sets in a way analogous to the definition of $C$-extremal sequences. We also characterize these sequences.

math.NT↗

arXiv2022

Extremal sequences for a weighted zero-sum constant

The constant $C_A(n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $\mathbb Z_n$ has a subsequence of consecutive terms whose $A$-weighted sum is zero, where the weight set $A\subseteq \mathbb Z_n\setminus \{0\}$. If $C_A(n)=k$, then a sequence in $\mathbb Z_n$ of length $k-1$ which has no $A$-weighted zero-sum subsequence of consecutive terms is called an $A$-extremal sequence. We characterize these sequences for some particular weight sets.

math.NT↗

arXiv2022

Extremal sequences for the unit-weighted Gao constant of $\mathbb Z_n$

For $A\subseteq \mathbb Z_n$, the $A$-weighted Gao constant $E_A(n)$ is defined to be the smallest natural number $k$, such that any sequence of $k$ elements in $\mathbb Z_n$ has a subsequence of length $n$, whose $A$-weighted sum is zero. Sequences of length $E_A(n)-1$ in $\mathbb Z_n$, which do not have any $A$-weighted zero-sum subsequence of length $n$ are called $A$-extremal sequences for the Gao constant. Such a sequence which has $n-1$ zeroes is said to be of the standard type. When $A=U(n)$ (units in $\mathbb Z_n$) where $n$ is odd, we characterize all such sequences and show that they are of the standard type. When $n$ is even, we give examples of such sequences which are not of the standard type. We also characterize the $U(n)$-extremal sequences for the Gao constant, when $n=2^rp$, where $p$ is an odd prime.

math.NT↗