arXiv subjects

Khushboo Agarwal

Publications and source records attributed to Khushboo Agarwal.

15 recordsLinked to original sources

arXiv2026

Sub-wavelength mid-infrared imaging of locally driven photocurrents using diamond campanile probes

Precise and high efficiency concentration of mid-infrared (mid-IR) light into sub wavelength volumes is essential for probing low-energy excitations and achieving strong field enhancements, which can be hindered by absorption losses and coupling inefficiencies at long wavelengths. Here, we introduce an innovative diamond-based metal-insulator-metal campanile probe that adiabatically compresses free-space mid infrared light (10 \mum) into \approx 1 \mum domains. Integrated into a scanning photovoltage microscope, the probe enables sub-wavelength mapping of locally driven photocurrents in graphene, resolving polarization dependent and contact-sensitive responses at energies down to \approx 0.1 eV. Experiments reveal a photocurrent signal density enhancement of 10^3 and coupling efficiencies approaching 80%, in agreement with numerical simulations. Operation of the probe with quantum cascade and free electron lasers demonstrates a robust, spectrally tunable platform for high-resolution exploration of low-energy carrier dynamics in atomically thin materials, opening opportunities for mid-IR optoelectronics and quantum photonics.

cond-mat.mes-hall↗

arXiv2026

Games with Rational and Herding Players

Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate reasoning. In this paper, we develop an analytical framework to study large population games with an alpha-fraction of rational and (1-alpha)-fraction of herding players. We introduce a new notion of equilibrium called alpha-Rational Nash Equilibrium (in short, alpha-RNE) and discuss its interpretations. Some classical equilibria may disappear, and some new ones may emerge, but only for smaller alpha >0. Interestingly, rational players benefit from the presence of herding and may even achieve utility exceeding the socially optimum. Even more strikingly, in some cases, the herding players also benefit, attaining utility close to the social optimum. We further study the effect of the herding fraction on system performance using measures such as the Price of Anarchy (PoA). In transportation networks, a well-known paradox first studied by Pigou and later by Braess typically arises from rational decision-making: adding an extra link can reduce overall efficiency. Our analysis leads to a different conclusion. When a substantial fraction of users exhibit herding behavior, introducing a new link can increase efficiency, provided herding choices can be suitably influenced. The gains are larger when the herding fraction is higher and/or congestion is lower. By contrast, when herding decisions cannot be influenced, the added link may become detrimental. We also study a bandwidth sharing game in which herding tendencies improve system efficiency. Finally, we discuss the mechanism or influence design in the presence of herding, highlighting both opportunities and risks.

math.OC↗

arXiv2025

Thermal transport mapping in twisted double bilayer graphene

Two-dimensional (2D) materials have attracted significant interest due to their tunable physical properties when stacked into homo- and hetero-structures. Twisting adjacent layers introduces moiré patterns that strongly influence the material electronic and thermal behavior. In twisted graphene systems, the twist angle critically alters phonon transport, leading to reduced thermal conductivity compared to Bernal-stacked configurations. However, experimental investigations into thermal transport in twisted structures remain limited. Here, we study the local thermal properties of twisted double bilayer graphene (TDBG) using Scanning Thermal Microscopy (SThM). We find an increase in thermal resistance of $0.3 \pm 0.1 \times 10^6 KW^{-1}$ compared to untwisted bilayers, attributed to changes in both intrinsic thermal conductivity and the tip-sample interface. These results, supported by analytical modeling, provide new insight into thermal transport mechanisms in twisted 2D systems and offer a pathway toward thermal engineering in twistronic devices.

cond-mat.mes-hall↗

arXiv2025

Queue or lounge: strategic design for strategic customer

Considering an M/M/1 queue with an additional lounge facility (LF), the quest of this paper is to understand the instances when LF is an attractive option, from customer perspective as well as from system perspective: will the customers choose to join the queue or prefer to detour briefly to lounge? In reality, customers do not perform complex computations for such tasks, but instead choose based on some heuristics. We further assume that the customers pessimistically anticipate the future congestion while making the choice. Our analysis reveals that the customers use the LF only when the queue is too crowded, and the lounge is relatively empty; however, strikingly, the customer choice is more inclined towards rejection for the LF in systems with higher traffic (load). We also explore an optimization problem where the system determines whether to implement an LF and what capacity it should have, while accounting for customers' behavioral responses. Under low load conditions, the system benefits from designing a high-capacity lounge, and the customers also prefer to use the LF actively. Surprisingly, neither the system prefers big LF, nor the customers prefer to use the LF profusely at high load conditions; optimal for either is to use the LF sparingly. Thus, importantly, the strategic system and the bounded-rational customers are not in a tug-of-war situation.

math.OC↗

arXiv2024

Limiting behaviour of Branching Processes and Online Social Networks

The literature considers multi-type Markov branching processes (BPs), where the offspring distribution depends only on the living (current) population. We analyse the total-current population-dependent BPs where the offspring distribution can also depend on the total (dead and living) population. Such a generalization is inspired by the need to accurately model content propagation over online social networks (OSNs). The key question investigated is the time-asymptotic proportion of the populations, which translates to the proportional visibility of the posts on the OSN. We provide the answer using a stochastic approximation (SA) technique, which has not been used in the existing BP literature. The analysis is derived using a non-trivial autonomous measurable ODE. Interestingly, we prove the possibility of a new limiting behaviour for the stochastic trajectory, named as hovering around. Such a result is not just new to the theory of BPs but also to the SA based literature. Later, we explore three new variants of BPs: (i) any living individual of a population can attack and acquire the living individuals of the other population, in addition to producing its offspring; (ii) the individuals can die due to abnormal circumstances, and not just at the completion of their lifetimes; (iii) the expected number of offspring decreases as the total-population increases, leading to the saturation of the total-population. Such variants aid in analysing unexplored aspects of content propagation over OSNs: (i) competition in advertisement posts for similar products; (ii) controlling fake-post propagation, while not affecting the sharing of real-post; (iii) impact of re-forwarding the posts. We also designed and analysed a participation (mean-field) game where the OSN lures the users with a reward-based scheme to provide their opinion about the actuality of the post (fake or real).

math.PR↗

arXiv2024

Balancing rationality and social influence: Alpha-rational Nash equilibrium in games with herding

The classical game theory models rational players and proposes Nash equilibrium (NE) as the solution. However, real-world scenarios rarely feature rational players; instead, players make inconsistent and irrational decisions. Often, irrational players exhibit herding behaviour by simply following the majority. In this paper, we consider the mean-field game with $α$-fraction of rational players and the rest being herding-irrational players. For such a game, we introduce a novel concept of equilibrium named $α$-Rational NE (in short, $α$-RNE). The $α$-RNEs and their implications are extensively analyzed in the game with two actions. Due to herding-irrational players, new equilibria may arise, and some classical NEs may be deleted. The rational players are not harmed but benefit from the presence of irrational players. Notably, we demonstrate through examples that rational players leverage upon the herding behaviour of irrational players and may attain higher utility (under $α$-RNE) than social optimal utility (in the classical setting). Interestingly, the irrational players may also benefit by not being rational. We observe that irrational players do not lose compared to some classical NEs for participation and bandwidth sharing games. More importantly, in bandwidth sharing game, irrational players receive utility that approaches the social optimal utility. Such examples indicate that it may sometimes be `rational' to be irrational.

cs.GT↗

arXiv2024

Quantifying the local mechanical properties of twisted double bilayer graphene

Nanomechanical measurements of minimally twisted van der Waals materials remained elusive despite their fundamental importance for device realisation. Here, we use Ultrasonic Force Microscopy (UFM) to locally quantify the variation of out-of-plane Young's modulus in minimally twisted double bilayer graphene (TDBG). We reveal a softening of the Young's modulus by 7\% and 17\% along single and double domain walls, respectively. Our experimental results are confirmed by force-field relaxation models. This study highlights the strong tunability of nanomechanical properties in engineered twisted materials, and paves the way for future applications of designer 2D nanomechanical systems.

cond-mat.mes-hall↗

arXiv2023

Robust fake-post detection against real-coloring adversaries

The viral propagation of fake posts on online social networks (OSNs) has become an alarming concern. The paper aims to design control mechanisms for fake post detection while negligibly affecting the propagation of real posts. Towards this, a warning mechanism based on crowd-signals was recently proposed, where all users actively declare the post as real or fake. In this paper, we consider a more realistic framework where users exhibit different adversarial or non-cooperative behaviour: (i) they can independently decide whether to provide their response, (ii) they can choose not to consider the warning signal while providing the response, and (iii) they can be real-coloring adversaries who deliberately declare any post as real. To analyze the post-propagation process in this complex system, we propose and study a new branching process, namely total-current population-dependent branching process with multiple death types. At first, we compare and show that the existing warning mechanism significantly under-performs in the presence of adversaries. Then, we design new mechanisms which remarkably perform better than the existing mechanism by cleverly eliminating the influence of the responses of the adversaries. Finally, we propose another enhanced mechanism which assumes minimal knowledge about the user-specific parameters. The theoretical results are validated using Monte-Carlo simulations.

math.PR↗

arXiv2023

Tuning thermoelectric properties of Sb$_2$Te$_3$-AgSbTe$_2$ nanocomposite thin film -- synergy of band engineering and heat transport modulation

The present study demonstrates a large enhancement in the Seebeck coefficient and ultralow thermal conductivity (TE) in Sb$_2$Te$_3$-AgSbTe$_2$ nanocomposite thin film. The addition of Ag leads to the in-situ formation of AgSbTe$_2$ secondary phase nanoaggregates in the Sb$_2$Te$_3$ matrix during the growth resulting in a large Seebeck coefficient and reduction of the thermal conductivity. A series of samples with different amounts of minor AgSbTe$_2$ phases are prepared to optimize the TE performance of Sb$_2$Te$_3$ thin films. Based on the experimental and theoretical evidence, it is concluded that a small concentration of Ag promotes the band flattening and induces a sharp resonate-like state deep inside the valence band of Sb$_2$Te$_3$, concurrently modifying the density of states (DOS) of the composite sample. In addition, the electrical potential barrier introduced by the band offset between the host TE matrix and the secondary phases promotes strong energy-dependent carrier scattering in the composite sample, which is also responsible for enhanced TE performance. A contemporary approach based on scanning thermal microscopy is performed to experimentally obtain thermal conductivity values of both the in-plane and cross-plane directions, showing a reduced in-plane thermal conductivity value by ~ 58% upon incorporating the AgSbTe$_2$ phase in the Sb$_2$Te$_3$ matrix. Benefitting from the synergistic manipulation of electrical and thermal transport, a large ZT value of 2.2 is achieved at 375 K. The present study indicates the importance of a combined effect of band structure modification and energy-dependent charge carrier scattering along with reduced thermal conductivity for enhancing TE properties.

cond-mat.mtrl-sci↗

arXiv2023

New results in Branching processes using Stochastic Approximation

We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation techniques, we show that the time-asymptotic proportion of the populations either converges to the equilibrium points or infinitely often enters every neighbourhood and exits some neighbourhood of a saddle point of an appropriate ordinary differential equation with a certain probability (almost surely for the process with attack and proportion-dependent branching process). The result holds under finite second-moment conditions. We also show that certain normalized trajectories of the embedded chain almost surely converge to the solution of the ordinary differential equation uniformly over any finite time window as time progresses. In addition to extending the analysis of several existing BPs, we analyze two new variants: BP with attack and acquisition, and BP with proportion-dependent offspring. Using these results, we study competition in viral markets and fake news control on online social networks.

math.PR↗

arXiv2023

Single-out fake posts: participation game and its design

Crowd-sourcing models, which leverage the collective opinions/signals of users on online social networks (OSNs), are well-accepted for fake post detection; however, motivating the users to provide the crowd signals is challenging, even more so in the presence of adversarial users. We design a participation (mean-field) game where users of the OSN are lured by a reward-based scheme to provide the binary (real/fake) signals such that the OSN achieves $(θ, δ)$-level of actuality identification (AI) - not more than $δ$ fraction of non-adversarial users incorrectly judge the real post, and at least $θ$ fraction of non-adversarial users identify the fake post as fake. An appropriate warning mechanism is proposed to influence the decision-making of the users such that the resultant game has at least one Nash Equilibrium (NE) achieving AI. We also identify the conditions under which all NEs achieve AI. Further, we numerically illustrate that one can always design an AI game if the normalized difference in the innate identification capacities of the users is at least $1\%$, when desired $θ= 75\%$.

math.OC↗

arXiv2022

Saturated total-population dependent branching process and viral markets

Interesting posts are continually forwarded by the users of the online social network (OSN). Such propagation leads to re-forwarding of the post to some of the previous recipients, which increases as the post reaches a large number of users. Consequently, the effective forwards (after deleting the re-forwards) reduce, eventually leading to the saturation of the total number of copies. We model this process as a new variant of the branching process, the `saturated total-population-dependent branching process', and analyse it using the stochastic approximation technique. Notably, we obtain deterministic trajectories which approximate the total and unread copies of the post `asymptotically and almost surely' over any finite time window; this trajectory depends only on four parameters related to the network characteristics. Further, we provide expressions for the peak unread copies, maximum outreach and the life span of the post. We observe known exponential growth but with time-varying rates. We also validate our theory through detailed simulations on the SNAP Twitter dataset.

math.PR↗

arXiv2022

Controlling Fake News by Tagging: A Branching Process Analysis

The spread of fake news on online social networks (OSNs) has become a matter of concern. These platforms are also used for propagating important authentic information. Thus, there is a need for mitigating fake news without significantly influencing the spread of real news. We leverage users' inherent capabilities of identifying fake news and propose a warning-based control mechanism to curb this spread. Warnings are based on previous users' responses that indicate the authenticity of the news. We use population-size dependent continuous-time multi-type branching processes to describe the spreading under the warning mechanism. We also have new results towards these branching processes. The (time) asymptotic proportions of the individual populations are derived using stochastic approximation tools. Using these, relevant type 1, type 2 performances are derived and an appropriate optimization problem is solved. The proposed mechanism effectively controls fake news, with negligible influence on the propagation of authentic news. We validate performance measures using Monte Carlo simulations on network connections provided by Twitter data.

cs.SI↗

arXiv2021

Evolutionary Vaccination Games with premature vaccines to combat ongoing deadly pandemic

We consider a vaccination game that results with the introduction of premature and possibly scarce vaccines introduced in a desperate bid to combat the otherwise ravaging deadly pandemic. The response of unsure agents amid many uncertainties makes this game completely different from the previous studies. We construct a framework that combines SIS epidemic model with a variety of dynamic behavioral vaccination responses and demographic aspects. The response of each agent is influenced by the vaccination hesitancy and urgency, which arise due to their personal belief about efficacy and side-effects of the vaccine, disease characteristics, and relevant reported information (e.g., side-effects, disease statistics etc.). Based on such aspects, we identify the responses that are stable against static mutations. By analysing the attractors of the resulting ODEs, we observe interesting patterns in the limiting state of the system under evolutionary stable (ES) strategies, as a function of various defining parameters. There are responses for which the disease is eradicated completely (at limiting state), but none are stable against mutations. Also, vaccination abundance results in higher infected fractions at ES limiting state, irrespective of the disease death rate.

math.DS↗

arXiv2020

Branching Process with Attack: Viral Competing Markets

The marked increase in advertisements over online social networks (OSNs) necessitates the study of content propagation. We analyse the viral markets with content providers competing for the propagation of similar posts over OSNs. Towards this, we required a new variant of the branching process (BP), which we named as "Branching process with attack"; the entities upon wake up attempt to attack and acquire the opposite population; furthermore, each entity produces its offsprings as is usually considered in BPs. In addition to providing expressions for the growth rates of individual posts, dichotomy etc., we explore the co-existence of posts; can the competing content spread and explode (number of unread/live copies of both posts grow significantly with time) simultaneously over the network? We prove that either one or both populations/posts get extinct or the populations settle to a unique co-existence equilibrium and derive the corresponding asymptotic ratios of the two populations/posts. Our analysis applies to large population networks focusing on mass behaviour, rather than micro details. Our study provides insights into two crucial design aspects, the number of seed users and the quality of the post.

cs.SI↗