publications
publications by categories in reversed chronological order. generated by jekyll-scholar.
2025
- SubmittedA flow-kick model of dryland vegetation patterns: the impact of rainfall variability on resiliencePunit Gandhi, Matthew Oline, and Mary Silber2025
In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by harvesting additional stormwater from upslope low-infiltration bare zones. We are interested in the robustness of this pattern formation survival mechanism to changes in rainfall variability. For this, we use a flow-kick modeling framework that treats storms as instantaneous kicks to the soil water. The positive feedbacks in the storm-level hydrology, that act to concentrate water within the vegetation bands, are captured through the spatial profiles of the soil water kicks. Between storms, the soil water and vegetation, modeled by a two-component reaction-diffusion system, evolve together. We use a combination of linear stability analysis and numerical simulation to compare predictions of idealized periodic rainfall, with no variability, to predictions when there is randomness in the timing and magnitude of water input from storms. We show that including these random elements leads to a decrease in the parameter range over which patterns appear. This suggests that an increase in storm variability, even with the same mean annual rainfall, may negatively impact the resilience of these pattern-forming dryland ecosystems.
@misc{gandhi2025flowkickmodeldrylandvegetation, title = {A flow-kick model of dryland vegetation patterns: the impact of rainfall variability on resilience}, author = {Gandhi, Punit and Oline, Matthew and Silber, Mary}, year = {2025}, eprint = {2501.01569}, archiveprefix = {arXiv}, primaryclass = {nlin.PS}, url = {https://arxiv.org/abs/2501.01569} } - Math. Biosci.Characterizing symmetry transitions in systems with dynamic morphologyMathematical Biosciences, 2025
The accurate quantification of symmetry is a key goal in biological inquiries because symmetry can affect biological performance and can reveal insights into development and evolutionary history. Recently, we proposed a versatile measure of symmetry, transformation information (TI), which provides an entropy-based measure of deviations from exact symmetry with respect to a parameterized family of transformations. Here we develop this measure further to quantify approximate symmetries and maximal symmetries represented by critical points in TI as a function of a transformation parameter. This framework allows us to characterize the evolution of symmetry by tracking qualitative changes with respect to these critical points. We apply TI to increasingly complex settings, from mathematically tractable probability distributions to differential equation models with emergent behaviors that are inspired by developmental biology and formulated in both static and growing domains. Our analysis of the qualitative changes in symmetry properties indicates a potential pathway toward a general mathematical framework for characterizing symmetry transitions akin to bifurcation theory for dynamical systems. The results reveal deep connections between observed symmetry transitions, subtle changes in morphology, and the underlying mechanisms that govern the dynamics of the system.
@article{ciocanel2025characterizing, title = {Characterizing symmetry transitions in systems with dynamic morphology}, journal = {Mathematical Biosciences}, volume = {384}, pages = {109431}, year = {2025}, issn = {0025-5564}, doi = {https://doi.org/10.1016/j.mbs.2025.109431}, url = {https://www.sciencedirect.com/science/article/pii/S0025556425000574}, author = {Ciocanel, M.-Veronica and Gandhi, Punit and Niklas, Karl and Dawes, Adriana T.}, keywords = {Approximate symmetry, Developmental biology, Information theory, Bifurcations, Pattern formation} } - Math. Biosci.A conceptual framework for modeling a latching mechanism for cell cycle regulationPunit Gandhi and Yangyang WangMathematical Biosciences, 2025
Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.
@article{gandhi2025conceptual, title = {A conceptual framework for modeling a latching mechanism for cell cycle regulation}, journal = {Mathematical Biosciences}, volume = {382}, pages = {109396}, year = {2025}, issn = {0025-5564}, doi = {https://doi.org/10.1016/j.mbs.2025.109396}, url = {https://www.sciencedirect.com/science/article/pii/S0025556425000227}, author = {Gandhi, Punit and Wang, Yangyang}, keywords = {Coupled oscillators, Cell cycle regulation, Homoclinic bifurcation, Symmetry breaking, Bifurcation} }
2023
- SIADSA Pulsed-Precipitation Model of Dryland Vegetation Pattern FormationPunit Gandhi, Lily Liu, and Mary SilberSIAM Journal on Applied Dynamical Systems, 2023
Abstract. We develop a model for investigating the impact of rainstorm variability on the formation of banded vegetation patterns in dryland ecosystems. Water input, during rare rainstorms, is modeled as an instantaneous kick to the soil water. The redistribution, from surface water to soil moisture, accounts for the impact of vegetation on infiltration rate and downslope overland flow speed. These two positive feedbacks between water and biomass distributions act on the fast timescales of rain storms. During dry periods, a classic reaction-diffusion framework is used for the slow processes associated with soil water and biomass. This pulsed-precipitation model predicts that the preferred spacing of the vegetation bands is determined by the characteristic distance that a storm pulse of water travels overland before infiltrating into the soil. In this way, the vegetation pattern is determined by the fast ecohydrological processes and may be attuned with its dryland precipitation pattern. We demonstrate how this modeling framework, suited for stochastic rain inputs, can be used to investigate possible collapse of a dryland pattern-forming ecosystem under different precipitation patterns with identical low annual mean. Model simulations suggest, for instance, that shorter rainy seasons and greater variability in storm depth may both hasten ecosystem collapse.
@article{gandhi2023pulsed, author = {Gandhi, Punit and Liu, Lily and Silber, Mary}, title = {A Pulsed-Precipitation Model of Dryland Vegetation Pattern Formation}, journal = {SIAM Journal on Applied Dynamical Systems}, volume = {22}, number = {2}, pages = {657-693}, year = {2023}, doi = {10.1137/22M1469572}, url = {https://doi.org/10.1137/22M1469572}, eprint = {https://doi.org/10.1137/22M1469572} }
2022
- Lett. Biomath.Effects of contact tracing and self-reporting in a network disease modelPunit Gandhi, Michael A. Robert, John P. Palacios, and David ChanLetters in Biomathematics, 2022
Contact tracing can be an effective measure to control emerging infectious diseases, but the efficacy of contact tracing measures can depend upon the willingness of individuals to get be tested even when they are symptomatic. In this paper, we examine the effects of symptomatic individuals getting tested and the use of contact tracing in a network model of disease transmission. We utilize a network model to resolve the influence of contact patterns between individuals as apposed to assuming mass action where all individuals are connected to each other.  We find that the effects of self-reporting and contact tracing vary depending on the structure of the network. We also compare the results from the network model with an analogous ODE model that assumes mass action and demonstrate how the results can be dramatically different.
@article{gandhi2022contact, title = {Effects of contact tracing and self-reporting in a network disease model}, author = {Gandhi, Punit and Robert, Michael A. and Palacios, John P. and Chan, David}, journal = {Letters in Biomathematics}, volume = {9}, number = {1}, pages = {23--39}, year = {2022}, url = {https://lettersinbiomath.org/manuscript/index.php/lib/article/view/143}, doi = {10.30707/LiB9.1.1681913305.219107} }
2021
- Phil. Trans. AIdentification of approximate symmetries in biological developmentPhilosophical Transactions of the Royal Society A, 2021
Virtually all forms of life, from single-cell eukaryotes to complex, highly differentiated multicellular organisms, exhibit a property referred to as symmetry. However, precise measures of symmetry are often difficult to formulate and apply in a meaningful way to biological systems, where symmetries and asymmetries can be dynamic and transient, or be visually apparent but not reliably quantifiable using standard measures from mathematics and physics. Here, we present and illustrate a novel measure that draws on concepts from information theory to quantify the degree of symmetry, enabling the identification of approximate symmetries that may be present in a pattern or a biological image. We apply the measure to rotation, reflection and translation symmetries in patterns produced by a Turing model, as well as natural objects (algae, flowers and leaves). This method of symmetry quantification is unbiased and rigorous, and requires minimal manual processing compared to alternative measures. The proposed method is therefore a useful tool for comparison and identification of symmetries in biological systems, with potential future applications to symmetries that arise during development, as observed in vivo or as produced by mathematical models. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.
@article{gandhi2021approximate, author = {Gandhi, Punit and Ciocanel, M.-Veronica and Niklas, Karl and Dawes, Adriana T.}, title = {Identification of approximate symmetries in biological development}, journal = {Philosophical Transactions of the Royal Society A}, volume = {379}, number = {2213}, pages = {20200273}, year = {2021}, doi = {10.1098/rsta.2020.0273}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2020.0273}, eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2020.0273} }
2020
- SIADSBifurcations on fully inhomogeneous networksSIAM Journal on Applied Dynamical Systems, 2020
Center manifold reduction is a standard technique in bifurcation theory, reducing the essential features of local bifurcations to equations in a small number of variables corresponding to critical eigenvalues. This method can be applied to admissible differential equations for a network, but it bears no obvious relation to the network structure. A fully inhomogeneous network is one in which all nodes and couplings can be different. For this class of networks, there are general circumstances in which the center manifold reduced equations inherit a network structure of their own. This structure arises by decomposing the network into path components, which connect to each other in a feedforward manner. Critical eigenvalues can then be associated with specific components, and the network structure on the center manifold depends on how these critical components connect within the network. This observation is used to analyze codimension-1 and codimension-2 local bifurcations. For codimension-1, only one critical component is involved, and generic local bifurcations are saddle-node and standard Hopf. For codimension-2, we focus on the case when one component is downstream from the other in the feedforward structure. This gives rise to four cases: steady or Hopf upstream combined with steady or Hopf downstream. Here the generic bifurcations, within the realm of network-admissible equations, differ significantly from generic codimension-2 bifurcations in a general dynamical system. In each case, we derive singularity-theoretic normal forms and unfoldings, present bifurcation diagrams, and tabulate the bifurcating states and their stabilities.
@article{gandhi2020bifurcations, title = {Bifurcations on fully inhomogeneous networks}, author = {Gandhi, Punit and Golubitsky, Martin and Postlethwaite, Claire and Stewart, Ian and Wang, Yangyang}, journal = {SIAM Journal on Applied Dynamical Systems}, volume = {19}, number = {1}, pages = {366--411}, year = {2020}, publisher = {SIAM}, doi = {10.1137/18M1230736}, url = {https://doi.org/10.1137/18M1230736}, eprint = { https://doi.org/10.1137/18M1230736 } } - Physica DA fast–slow model of banded vegetation pattern formation in drylandsPunit Gandhi, Sara Bonetti, Sarah Iams, Amilcare Porporato, and Mary SilberPhysica D: Nonlinear Phenomena, 2020
From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple timescales. We propose a new fast–slow switching model in order to capture these processes on appropriate timescales within a conceptual modeling framework based on reaction–advection–diffusion equations. The fast system captures hydrological processes that occur on minute to hour timescales during and shortly after major rainstorms, assuming a fixed vegetation distribution. These include key feedbacks between vegetation biomass and downhill surface water transport, as well as between biomass and infiltration rate. The slow system acts between rain events, on a timescale of days to months, and evolves vegetation and soil moisture. Modeling processes at the appropriate timescales allows parameter values to be set by the actual processes they capture. This reduces the number of parameters that are chosen expressly to fit pattern characteristics, or to artificially slow down fast processes by the orders of magnitude required to align their timescales with the biomass dynamics. We explore the fast–slow switching model through numerical simulation on a one-dimensional hillslope, and find agreement with certain observations about the pattern formation phenomenon, including band spacing and upslope colonization rates. We also find that the predicted soil moisture dynamics are consistent with time series data that has been collected at a banded vegetation site. This fast–slow model framework introduces a tool for investigating the possible impact of changes to frequency and intensity of rain events in dryland ecosystems.
@article{gandhi2020fast, title = {A fast--slow model of banded vegetation pattern formation in drylands}, author = {Gandhi, Punit and Bonetti, Sara and Iams, Sarah and Porporato, Amilcare and Silber, Mary}, journal = {Physica D: Nonlinear Phenomena}, volume = {410}, pages = {132534}, year = {2020}, publisher = {Elsevier}, keywords = {Pattern formation, Vegetation bands, Dryland ecohydrology, Reaction–advection–diffusion equations, fast–slow switching model}, issn = {0167-2789}, doi = {https://doi.org/10.1016/j.physd.2020.132534}, url = {https://www.sciencedirect.com/science/article/pii/S0167278919307328} }
2019
- SpringerVegetation Pattern Formation in DrylandsPunit Gandhi, Sarah Iams, Sara Bonetti, and Mary Silber2019
This chapter aims to (1) provide background for conceptual mathematical models of spontaneous pattern formation, in the context of dryland vegetation patterns, and (2) review observational studies of the phenomenon. The chapter also highlights challenges and opportunities associated with the development of the models in light of increasing availability of remote sensing data. This includes both satellite imagery of the patterns and elevation data of the topography. The vast scales, in time and space, associated with the key processes further suggest avenues for improved mathematical modeling paradigms.
@inbook{gandhi2019vegetation, author = {Gandhi, Punit and Iams, Sarah and Bonetti, Sara and Silber, Mary}, editor = {D'Odorico, Paolo and Porporato, Amilcare and Wilkinson Runyan, Christiane}, title = {Vegetation Pattern Formation in Drylands}, booktitle = {Dryland Ecohydrology}, year = {2019}, publisher = {Springer International Publishing}, address = {Cham}, pages = {469--509}, isbn = {978-3-030-23269-6}, doi = {10.1007/978-3-030-23269-6_18}, url = {https://doi.org/10.1007/978-3-030-23269-6_18} }
2018
- Phil. Trans. ASpatially localized structures in the Gray–Scott modelPunit Gandhi, Yuval R. Zelnik, and Edgar KnoblochPhilosophical Transactions of the Royal Society A, 2018
Spatially localized structures in the one-dimensional Gray–Scott reaction–diffusion model are studied using a combination of numerical continuation techniques and weakly nonlinear theory, focusing on the regime in which the activator and substrate diffusivities are different but comparable. Localized states arise in three different ways: in a subcritical Turing instability present in this regime, and from folds in the branch of spatially periodic Turing states. They also arise from the fold of spatially uniform states. These three solution branches interconnect in complex ways. We use numerical continuation techniques to explore their global behaviour within a formulation of the model that has been used to describe dryland vegetation patterns on a flat terrain. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.
@article{gandhi2018spatially, title = {Spatially localized structures in the Gray--Scott model}, author = {Gandhi, Punit and Zelnik, Yuval R. and Knobloch, Edgar}, journal = {Philosophical Transactions of the Royal Society A}, volume = {376}, number = {2135}, pages = {20170375}, year = {2018}, publisher = {The Royal Society Publishing}, doi = {10.1098/rsta.2017.0375}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0375}, eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2017.0375} } - R. Soc. InterfaceA topographic mechanism for arcing of dryland vegetation bandsPunit Gandhi, Lucien Werner, Sarah Iams, Karna Gowda, and Mary SilberRoyal Society Interface, 2018
Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with the stripes aligned transverse to the elevation gradient. In many cases, these vegetation bands are arced, with field observations suggesting a link between the orientation of arcing relative to the grade and the curvature of the underlying terrain. We modify the water transport in the Klausmeier model of water–biomass interactions, originally posed on a uniform hillslope, to qualitatively capture the influence of terrain curvature on the vegetation patterns. Numerical simulations of this modified model indicate that the vegetation bands arc convex-downslope when growing on top of a ridge, and convex-upslope when growing in a valley. This behaviour is consistent with observations from remote sensing data that we present here. Model simulations show further that whether bands grow on ridges, valleys or both depends on the precipitation level. A survey of three banded vegetation sites, each with a different aridity level, indicates qualitatively similar behaviour.
@article{gandhi2018topographic, title = {A topographic mechanism for arcing of dryland vegetation bands}, author = {Gandhi, Punit and Werner, Lucien and Iams, Sarah and Gowda, Karna and Silber, Mary}, journal = {Royal Society Interface}, volume = {15}, number = {147}, pages = {20180508}, year = {2018}, doi = {10.1098/rsif.2018.0508}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsif.2018.0508}, eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2018.0508} } - ChaosImplications of tristability in pattern-forming ecosystemsYuval R. Zelnik, Punit Gandhi, Edgar Knobloch, and Ehud MeronChaos: An Interdisciplinary Journal of Nonlinear Science, Mar 2018
Many ecosystems show both self-organized spatial patterns and multistability of possible states. The combination of these two phenomena in different forms has a significant impact on the behavior of ecosystems in changing environments. One notable case is connected to tristability of two distinct uniform states together with patterned states, which has recently been found in model studies of dryland ecosystems. Using a simple model, we determine the extent of tristability in parameter space, explore its effects on the system dynamics, and consider its implications for state transitions or regime shifts. We analyze the bifurcation structure of model solutions that describe uniform states, periodic patterns, and hybrid states between the former two. We map out the parameter space where these states exist, and note how the different states interact with each other. We further focus on two special implications with ecological significance, breakdown of the snaking range and complex fronts. We find that the organization of the hybrid states within a homoclinic snaking structure breaks down as it meets a Maxwell point where simple fronts are stationary. We also discover a new series of complex fronts between the uniform states, each with its own velocity. We conclude with a brief discussion of the significance of these findings for the dynamics of regime shifts and their potential control.
@article{zelnik2018implications, author = {Zelnik, Yuval R. and Gandhi, Punit and Knobloch, Edgar and Meron, Ehud}, title = {Implications of tristability in pattern-forming ecosystems}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {28}, number = {3}, pages = {033609}, year = {2018}, month = mar, issn = {1054-1500}, doi = {10.1063/1.5018925}, url = {https://doi.org/10.1063/1.5018925}, eprint = {https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/1.5018925/14617421/033609\_1\_online.pdf} } - Phys. Teach.A Tale of Two Slinkies: Learning about Model Building in a Student-Driven ClassroomCalvin Berggren, Punit Gandhi, Jesse A. Livezey, and Ryan OlfThe Physics Teacher, Mar 2018
We describe a set of conceptual and hands-on activities based around understanding the dynamics of a Slinky that is hung vertically and released from rest. This Slinky drop experiment typically lasts a fraction of a second, but when observed in slow motion, one sees the Slinky compress from the top down while the bottom portion remains at rest—naively seeming to defy gravity—until the Slinky has completed its collapse. The motion, or lack thereof, of the bottom of the Slinky after the top is released sparks student curiosity by challenging expectations and provides motivation and context for learning about scientific model building.
@article{berggren2018tale, author = {Berggren, Calvin and Gandhi, Punit and Livezey, Jesse A. and Olf, Ryan}, title = {A Tale of Two Slinkies: Learning about Model Building in a Student-Driven Classroom}, journal = {The Physics Teacher}, volume = {56}, number = {3}, pages = {134-137}, year = {2018}, month = mar, issn = {0031-921X}, doi = {10.1119/1.5025285}, url = {https://doi.org/10.1119/1.5025285}, eprint = {https://pubs.aip.org/aapt/pte/article-pdf/56/3/134/9868214/134\_1\_online.pdf} }
2017
- Phys. Rev. FluidsSlanted snaking of localized Faraday wavesPhysical Review Fluids, Mar 2017
We report on an experimental, theoretical, and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the presence of a hysteretic transition to spatially extended parametrically excited surface waves when the acceleration amplitude is varied, as well as the presence of spatially localized waves exhibiting slanted snaking. The latter extend outside the hysteresis loop. We attribute this behavior to the presence of a conserved quantity, the liquid volume trapped within the meniscus, and introduce a universal model based on symmetry arguments, which couples the wave amplitude with such a conserved quantity. The model captures both the observed slanted snaking and the presence of localized waves outside the hysteresis loop, as demonstrated by numerical integration of the model equations.
@article{pradenas2017slanted, title = {Slanted snaking of localized {F}araday waves}, author = {Pradenas, Basti\'an and Araya, Isidora and Clerc, Marcel G. and Falc\'on, Claudio and Gandhi, Punit and Knobloch, Edgar}, journal = {Physical Review Fluids}, volume = {2}, issue = {6}, pages = {064401}, numpages = {12}, year = {2017}, publisher = {American Physical Society}, doi = {10.1103/PhysRevFluids.2.064401}, url = {https://link.aps.org/doi/10.1103/PhysRevFluids.2.064401} }
2016
- SpringerTime-periodic forcing of spatially localized structuresPunit Gandhi, Cédric Beaume, and Edgar KnoblochIn Nonlinear Dynamics: Materials, Theory and Experiments, Mar 2016
We study localized statesLocalized statesin the Swift–Hohenberg equation when time-periodic parametric forcing is introduced. The presence of a time-dependent forcing introduces a new characteristic time which creates a series of resonances with the depinning time of the fronts bounding the localized pattern. The organization of these resonances in parameter space can be understood using appropriate asymptotics. A number of distinct canard trajectories involved in the observed transitions is constructed.
@incollection{gandhi2016time, year = {2016}, booktitle = {Nonlinear Dynamics: Materials, Theory and Experiments}, volume = {173}, series = {Springer Proceedings in Physics}, editor = {Clerc, Marcel G. and Tlidi, Mustafa}, title = {Time-periodic forcing of spatially localized structures}, url = {https://link.springer.com/chapter/10.1007/978-3-319-24871-4_23}, doi = {https://doi.org/10.1007/978-3-319-24871-4_23}, publisher = {Springer International Publishing}, author = {Gandhi, Punit and Beaume, C\'edric and Knobloch, Edgar}, pages = {303--316}, isbn = {978-3-319-24871-4} } - AJPAttending to experimental physics practices and lifelong learning skills in an introductory laboratory coursePunit R. Gandhi, Jesse A. Livezey, Anna M. Zaniewski, Daniel L. Reinholz, and Dimitri R. Dounas-FrazerAmerican Journal of Physics, Sep 2016
We have designed an introductory laboratory course that engaged first-year undergraduate students in two complementary types of iteration: (1) iterative improvement of experiments through cycles of modeling systems, designing experiments, analyzing data, and refining models and designs; and (2) iterative improvement of self through cycles of reflecting on progress, soliciting feedback, and implementing changes to study habits and habits of mind. The course consisted of three major activities: a thermal expansion activity, which spanned the first half of the semester; final research projects, which spanned the second half of the semester; and guided student reflections, which took place throughout the duration of the course. We describe our curricular designs and report examples of student work that demonstrate students’ iterative improvements in multiple contexts.
@article{gandhi2016attending, author = {Gandhi, Punit R. and Livezey, Jesse A. and Zaniewski, Anna M. and Reinholz, Daniel L. and Dounas-Frazer, Dimitri R.}, title = {Attending to experimental physics practices and lifelong learning skills in an introductory laboratory course}, journal = {American Journal of Physics}, volume = {84}, number = {9}, pages = {696-703}, year = {2016}, month = sep, issn = {0002-9505}, doi = {10.1119/1.4955147}, url = {https://doi.org/10.1119/1.4955147}, eprint = {https://pubs.aip.org/aapt/ajp/article-pdf/84/9/696/13107215/696\_1\_online.pdf} } - ThesisLocalized States in Driven Dissipative Systems with Time-Periodic ModulationPunit R. GandhiSep 2016
The generalized Swift-Hohenberg equation is used to study the persistence and decay of localized patterns in the presence of time-periodic parametric forcing in one and two dimensions. A localized state that was stable with constant forcing may begin to breathe under periodic forcing, i.e. grow for part of the forcing cycle via nucleation of new wavelengths of the pattern followed by wavelength annihilation during another part of the cycle. The breathing dynamics occur as the forcing parameter exits the region of stability of the localized pattern on either side and the fronts that define the edges of the state temporarily depin. The parameters of the forcing determine if there will be net growth, a balance, or net decay on average. A novel resonance phenomenon between the forcing period and the time required to nucleate one wavelength of the pattern outside the pinning region is identified. The resonances generate distinct regions in parameter space characterized by the net number of wavelengths gained or lost in one forcing cycle. Canard trajectories, in which the localized state follows an unstable solution branch for some amount of time before quickly jumping to a stable one, appear near the transitions between each region. In one dimension, the partitioning of the parameter space is well described by an asymptotic theory based on the wavelength nucleation/annihilation time near the boundaries of the region of stability. This theory leads to predictions that are qualitatively correct and, in some cases, provide quantitative agreement with numerical simulations. The underlying resonance mechanism is a more general phenomenon and is also studied in the context of coupled oscillator systems with a periodically modulated Adler equation as a simple model. A strikingly similar partitioning of the parameter space is observed, with the resonances occurring this time between the period of the frequency modulation and the time for the generation of a phase slip.
@phdthesis{gandhi2016thesis, author = {Gandhi, Punit R.}, year = {2016}, title = {Localized States in Driven Dissipative Systems with Time-Periodic Modulation}, journal = {ProQuest Dissertations and Theses}, pages = {193}, keywords = {Pure sciences; Coupled oscillators; Localized structures; Resonance; Time-periodic modulation; Physics; 0605:Physics}, isbn = {978-1-369-05731-7}, language = {English}, url = {http://proxy.library.vcu.edu/login?url=https://www.proquest.com/dissertations-theses/localized-states-driven-dissipative-systems-with/docview/1816189314/se-2} }
2015
- PREDynamics of phase slips in systems with time-periodic modulationPunit Gandhi, Edgar Knobloch, and Cédric BeaumePhysical Review E, Sep 2015
The Adler equation with time-periodic frequency modulation is studied. A series of resonances between the period of the frequency modulation and the time scale for the generation of a phase slip is identified. The resulting parameter space structure is determined using a combination of numerical continuation, time simulations, and asymptotic methods. Regions with an integer number of phase slips per period are separated by regions with noninteger numbers of phase slips and include canard trajectories that drift along unstable equilibria. Both high- and low-frequency modulation is considered. An adiabatic description of the low-frequency modulation regime is found to be accurate over a large range of modulation periods.
@article{gandhi2015periodic, title = {Dynamics of phase slips in systems with time-periodic modulation}, author = {Gandhi, Punit and Knobloch, Edgar and Beaume, C\'edric}, journal = {Physical Review E}, volume = {92}, number = {6}, pages = {062914}, year = {2015}, doi = {10.1103/PhysRevE.92.062914}, url = {https://link.aps.org/doi/10.1103/PhysRevE.92.062914} } - SIADSA new resonance mechanism in the Swift–Hohenberg equation with time-periodic forcingPunit Gandhi, Cédric Beaume, and Edgar KnoblochSIAM Journal on Applied Dynamical Systems, Sep 2015
The generalized Swift–Hohenberg equation with a quadratic-cubic nonlinearity is used to study the persistence and decay of localized patterns in the presence of time-periodic parametric forcing. A novel resonance phenomenon between the forcing period and the time required to nucleate one wavelength of the pattern outside the pinning region is identified. The resonance generates distinct regions in parameter space characterized by the net number of wavelengths gained or lost in one forcing cycle. These regions are well described by an asymptotic theory based on the wavelength nucleation/annihilation time near the boundaries of the pinning region. The resulting theory leads to predictions that are qualitatively correct and, in some cases, provide quantitative agreement with numerical simulations.
@article{gandhi2015new, title = {A new resonance mechanism in the {S}wift--{H}ohenberg equation with time-periodic forcing}, author = {Gandhi, Punit and Beaume, C\'edric and Knobloch, Edgar}, journal = {SIAM Journal on Applied Dynamical Systems}, volume = {14}, pages = {860--892}, year = {2015}, doi = {10.1137/14099468X}, url = {https://doi.org/10.1137/14099468X}, eprint = { https://doi.org/10.1137/14099468X} } - PRLLocalized states in periodically forced systemsPunit Gandhi, Edgar Knobloch, and Cédric BeaumePhysical Review Letters, Sep 2015
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing, related but time-dependent structures may result. These may consist of breathing localized patterns, or states that grow for part of the cycle via nucleation of new wavelengths of the pattern followed by wavelength annihilation during the remainder of the cycle. These two competing processes lead to a complex phase diagram whose structure is a consequence of a series of resonances between the nucleation time and the forcing period. The resulting diagram is computed for the periodically forced quadratic-cubic Swift–Hohenberg equation, and its details are interpreted in terms of the properties of the depinning transition for the fronts bounding the localized state on either side. The results are expected to shed light on localized states in a large variety of periodically driven systems.
@article{gandhi2015localized, title = {Localized states in periodically forced systems}, author = {Gandhi, Punit and Knobloch, Edgar and Beaume, C\'edric}, journal = {Physical Review Letters}, volume = {114}, number = {3}, pages = {034102}, year = {2015}, publisher = {APS}, doi = {10.1103/PhysRevLett.114.034102}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.114.034102} }
2013
- Uncertainty analysis for a simple thermal expansion experimentDimitri R. Dounas-Frazer, Punit R. Gandhi, and Geoffrey Z. IwataAmerican Journal of Physics, May 2013
We describe a simple experiment for measuring the thermal expansion coefficient of a metal wire and discuss how the experiment can be used as a tool for exploring the interplay of measurement uncertainty and scientific models. In particular, we probe the regimes of applicability of three models of the wire: stiff and massless, elastic and massless, and elastic and massive. Using both analytical and empirical techniques, we present the conditions under which the wire’s mass and elasticity can be neglected. By accounting for these effects, we measure Nichrome’s thermal expansion coefficient to be 17.1(1.3) μm/m⋅K, which is consistent with the accepted value at the 8% level.
- Oscillator seeding of a high gain harmonic generation free electron laser in a radiator-first configurationP. Gandhi, G. Penn, M. Reinsch, J. S. Wurtele, and W. M. FawleyPhys. Rev. ST Accel. Beams, Feb 2013
A longitudinally and transversely coherent, high repetition rate x-ray source with widely tunable wavelength is desired for a variety of experimental applications. A free electron laser (FEL) powered by an electron beam from a superconducting linac can reach the desired peak and average x-ray power levels with transverse coherence. However, generating longitudinally coherent x-ray pulses is a significant challenge, especially at high repetition rate. This paper presents a one-dimensional theoretical and numerical investigation of a method to achieve longitudinal coherence and high repetition rate simultaneously. We propose a “radiator-first” configuration, wherein an FEL oscillator follows a high gain harmonic generation (HGHG) FEL. The oscillator generates seed power that is directed upstream to initiate the HGHG process in a following electron bunch. This configuration allows for the generation of radiation at short wavelength, which is highly sensitive to energy spread, to occur before the longer wavelength oscillator, whose performance is not seriously degraded by the beam heating in the upstream radiator. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass, 1D map is derived using a semianalytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft x-ray FEL.