Modes Of Entrainment Research Articles

Shock-induced atomisation of a liquid metal droplet

The present study uses Galinstan as a test fluid to investigate the shock-induced atomisation of a liquid metal droplet in a high-Weber-number regime $(We \sim 400\unicode{x2013}8000)$ . Atomisation dynamics is examined for three test environments: oxidizing (Galinstan–air), inert (Galinstan–nitrogen) and conventional fluids (deionised water–air). Due to the readily oxidizing nature of liquid metals, their atomisation in an industrial scale system is generally carried out in inert atmosphere conditions. However, no previous study has considered gas-induced secondary atomisation of liquid metals in inert conditions. Due to experimental challenges associated with molten metals, laboratory scale models are generally tested for conventional fluids like deionised water, liquid fuels, etc. The translation of results obtained from conventional fluid to liquid metal atomisation is rarely explored. Here a direct multiscale spatial and temporal comparison is provided between the atomisation dynamics of conventional fluid and liquid metals under oxidizing and inert conditions. The liquid metal droplet undergoes breakup through the shear-induced entrainment mode for the studied range of Weber number values. The prevailing mechanism is explained based on the relative dominance of droplet deformation and Kelvin–Helmholtz wave formation. The study provides quantitative and qualitative similarities for the three test cases and explains the differences in morphology of fragmenting secondary droplets in the oxidizing test case (Galinstan–air) due to rapid oxidation of the fragmenting ligaments. A phenomenological framework is postulated for predicting the morphology of secondary droplets. The formation of flake-like secondary droplets in the Galinstan air test case is based on the oxidation rate of liquid metals and the properties of the oxide layer formed on the atomizing ligament surface.

Parametric effects of light acting via multiple photoreceptors contribute to circadian entrainment in Drosophila melanogaster.

Circadian rhythms in physiology and behaviour have near 24 h periodicities that must adjust to the exact 24 h geophysical cycles on earth to ensure adaptive daily timing. Such adjustment is called entrainment. One major mode of entrainment is via the continuous modulation of circadian period by the prolonged presence of light. Although Drosophila melanogaster is a prominent insect model of chronobiology, there is little evidence for such continuous effects of light in the species. In this study, we demonstrate that prolonged light exposure at specific times of the day shapes the daily timing of activity in flies. We also establish that continuous UV- and blue-blocked light lengthens the circadian period of Drosophila and provide evidence that this is produced by the combined action of multiple photoreceptors which, includes the cell-autonomous photoreceptor cryptochrome. Finally, we introduce ramped light cycles as an entrainment paradigm that produces light entrainment that lacks the large light-driven startle responses typically displayed by flies and requires multiple days for entrainment to shifted cycles. These features are reminiscent of entrainment in mammalian models systems and make possible new experimental approaches to understanding the mechanisms underlying entrainment in the fly.

Multiphase flow characteristics and gas loss in the shear layer on a ventilated supercavity wall

The shear flow on the large-scale gas–water wall inside a ventilated supercavity exhibits gas entrainment mode and determines the change law of the supercavity's gas loss, significantly impacting the shape and dynamics of the supercavity. Therefore, to develop an accurate prediction model and a ventilation control method for a supercavity under complex motion conditions, it is required to systematically and quantitatively study the shear flow characteristics and rules. This study calculates and comparatively analyzes the shear layers on either side of the supercavity wall based on numerical simulations of ventilated supercavitating flows in an unbounded field using the gas–vapor–water multi-fluid model. It is shown that the external shear layer with a very irregular outer boundary is considerably thinner than the internal shear layer. We further analyze the flow and distribution characteristics of all the phases in the shear layers with and without the influence of gravity. Our analysis confirms that all the phases exhibit a similar velocity change rule along the supercavity radial direction in the shear layer, whereas gas and water phases exhibit opposite radial phase distribution trends. It was also seen when natural cavitation occurs that the vapor phase is mainly distributed in the head of the supercavity. Moreover, at the same radial position, it was seen that the vapor velocity was higher than the gas velocity and slightly lower than the water velocity. Using the shear flow and phase distribution characteristics, a shear-layer gas loss model is established and validated for ventilated supercavitating flows.

From Continuity to Rhythm II : Adjustment and Entrainment

This work is the second part of the article “From Continuity to Rhythm” (Acta Semiotica, II, 3, 2022), where I set out to define rhythm as a semiotic concept. The cornerstones for such a definition are Victoria Santa Cruz’s concept of Rhythm as an active and continuous principle of integration, Landowski’s understanding of continuity, Leibniz’s notion of Harmony, the physical concept of entrainment, and the formal definition of feedback from engineering as a framework to understand manipulation, adjustment and entrainment. The main contributions are : 1) analysing the regimes of adjustment and manipulation in terms of feedback, 2) establishing a link between manipulation and adjustment, showing that the former is a simplification of the latter, 3) providing a semiotic definition of entrainment that considers five different dimensions, expressing manipulation and adjustment as specific modes of entrainment, 4) providing a semiotic definition of Rhythm as a dynamic unification process departing from Leibniz’s notion of Harmony, 5) questioning Leibniz’s Harmony in favor of an active view of Rhythm that not only produces order or common properties, but that actively strives to maintain them in virtue of feedback.

Influence of a soluble surfactant on the transition to tip streaming

We analyze experimentally the influence of a soluble surfactant on the onset of the tip streaming produced by hydrodynamic focusing. For this purpose, we consider the viscous entrainment mode of the selective withdrawal configuration for very different outer liquid viscosities. The minimum capillary number above which viscous entrainment can be produced is determined as a function of the surfactant concentration. We analyze the influence of the surfactant monolayer on the shape and velocity of the emitted liquid jet. The results show the importance of the monolayer dynamics for sufficiently small values of the outer liquid viscosity.

An experimental study of jet fires in pits

The explosion of underground pipelines could cause a big crater in which a gas leakage occurs to induce a large jet fire. The pit wall would significantly affect the leaked gas flow and the subsequent jet fire behavior. This paper presents a systematical investigation on such jet fire in a pit (JFP). A facility consisting of a jet fire apparatus and a rectangular pit, was designed for the experimental study. Phenomenon observation shows that the JFP can be divided into the impinging jet flame (IJF), transitive jet flame (TJF) and jet flame ejected from the pit top (JFEPT), due to the variation of the mode of air entrained into the pit with the nozzle exit velocity. A dimensionless heat release rate (HRR) coupling the pit geometrical property is developed to correlate the flame area in different pits, which clarifies the critical dimensionless HRR to distinguish the IJF, TJF and JFEPT. Using the dimensionless HRR, data fitting can well develop the correlation for the flame length of TJF and JFEPT, and the correlation is well validated by the small-scale and full-scale jet fires in irregular cuboid pits. The dimensionless HRR also can be used to well correlate the flame width. The radiative fraction of IJF still follows the law of the Froude number at the nozzle exit, while that of JFEPT should be predicted using the Froude number at the top opening of pit. As indicated by the variations of air entrainment mode and radiative fraction, the flame buoyancy gradually plays a more significant role than the nozzle exit momentum in the flame behavior, as the nozzle exit velocity increases to cause the evolution of JFP from IJF to JFEPT. In addition, a line source radiation model and two solid radiation models are proposed to predict the thermal radiation of JFP.

Drop breakup and entrainment in the updraft

AbstractThis study aims to investigate the characteristics of gas–liquid countercurrent contact processes. In spray towers or other applications, several drops containing pollutants are entrained by the updraft flue gas, which can easily cause environmental pollution. Traditionally, this drop entrainment phenomenon is alleviated by increasing the diameter of the drops. However, the breakup of a large drop would also cause drop entrainment to become serious, a process referred to as secondary atomization. Herein, we propose the boundary of three drop modes in the updraft: drop falling mode, reverse entrainment mode, and breakup entrainment mode. The critical Weber number (We) is the key dimensionless number marking the beginning of the drop breakup. The ratio of the drag force to gravity and We are proposed as criteria for the drop entrainment.

Review Article: Advances in modeling of bed particle entrainment sheared by turbulent flow

Bed particle entrainment by turbulent wall-shear flow is a key topic of interest in hydrodynamics because it plays a major role to govern the planetary morphodynamics. In this paper, the state-of-the-art review of the essential mechanisms governing the bed particle entrainment by turbulent wall-shear flow and their mathematical modeling is presented. The paper starts with the appraisal of the earlier multifaceted ideas in modeling the particle entrainment highlighting the rolling, sliding, and lifting modes of entrainment. Then, various modeling approaches of bed particle entrainment, such as deterministic, stochastic, and spatiotemporal approaches, are critically analyzed. The modeling criteria of particle entrainment are distinguished for hydraulically smooth, transitional, and rough flow regimes. In this context, the responses of particle size, particle exposure, and packing condition to the near-bed turbulent flow that shears the particles to entrain are discussed. From the modern experimental outcomes, the conceptual mechanism of particle entrainment from the viewpoint of near-bed turbulent coherent structures is delineated. As the latest advancement of the subject, the paper sheds light on the origin of the primitive empirical formulations of bed particle entrainment deriving the scaling laws of threshold flow velocity of bed particle motion from the perspective of the phenomenological theory of turbulence. Besides, a model framework that provides a new look on the bed particle entrainment phenomenon stemming from the stochastic-cum-spatiotemporal approach is introduced. Finally, the future scope of research is articulated with open questions.

Entrainment and mixing in lock-exchange gravity currents using simultaneous velocity-density measurements

Gravity currents modify their flow characteristics by entraining ambient fluid, which depends on a variety of governing parameters such as the initial density, Δρ, the total initial height of the fluid, H, and the slope of the terrain, α, from where it is released. It is imperative to study the entrainment dynamics of a gravity current in order to have a clear understanding of mixing transitions that govern the flow physics, the velocity mixing layer thickness, δu, and the density mixing layer thickness, δρ. Experiments were conducted in a lock-exchange facility in which the dense fluid was separated from the ambient lighter fluid using a gate. As the gate is released instantaneously, an energy conserving gravity current is formed, for which the only governing parameter is the Reynolds number defined as Re=Uhν, where U is the front velocity of the gravity current and h is the height of the current. In our study, the bulk Richardson number (inverse of Froude number, Fr), Rib = g′HUb2 = 1, takes a constant value for all the experiments, with Ub being the bulk velocity of the current defined as Ub = g′H. Simultaneous particle image velocimetry and planar laser induced fluorescence measurement techniques are employed to get the velocity and density statistics. Using the buoyancy conservation equation, a new flux-based method was formulated for calculating the entrainment coefficient, EF, near the front and head of the propagating gravity current for a Reynolds number range of Re ≈ 485-12 270 used in our experiments. At the head of the current, the results show a mixing transition at Re ≈ 2700 that is attributed to the flow transitioning from weak Holmboe waves to Kelvin-Helmholtz instabilities, in the form of Kelvin-Helmholtz vortex rolls. Following this mixing transition, the entrainment coefficient continued to increase with increasing Reynolds number owing to the occurrence of three-dimensional Kelvin-Helmholtz billows that promote further small-scale local mixing. Such a mixing transition indicates that a fully turbulent state is not reached even at Re = 12 270 and the amount of entrainment and ensuing mixing depends on the type of flow instability and presence of small-scale secondary structures. The entrainment dynamics were further substantiated using the ratio of δu and δρ. It was observed that δuδρ decreases with increasing Re and reaches a constant value of δuδρ≈ 1 at high values of Re. This trend is in contrast to the entrainment coefficient EF, which never reaches a constant value even at high enough Re. This disparity could be explained by the fact that EF accounts for small-scale scalar mixing, which is not captured by the ratio of mixing layer thicknesses. Experimentally, it was also observed that the EF value near the front of gravity current was 2-9 times higher than the head value depending on the value of the Reynolds numbers. At low Reynolds numbers, the entrainment near the front is an order of magnitude higher than the head and the value decreases with increasing Re. This could be attributed to different modes of entrainment near the front (dominated by vortical structures) and the head (dominated by turbulent flux exchange triggered by the nature of the flow instability). The results from this study improve our understanding of entrainment dynamics and would be useful in developing empirical parameterizations for mixing in stratified flows.

Entrainment of the Circadian Clock in Neural Stem Cells by Epidermal Growth Factor is Closely Associated with ERK1/2-mediated Induction of Multiple Clock-related Genes

The mitotic activity of certain tissues in the body is closely associated with circadian clock function. However, the effects of growth factors on the molecular clockwork are not fully understood. Stimulation of neural stem cells (NSCs) with epidermal growth factor (EGF), a well-known mitogen, is known to cause synchronized cell cycle progression with a period of approximately 24 h, closely associated with the Per2 gene expression rhythm. Here, we examined the effects of EGF on the molecular clockwork of NSCs. Treatment of cultured NSCs derived from embryonic mouse forebrain with EGF (20 ng/mL) caused a phase shift in the PER2::LUCIFERASE bioluminescence rhythm in a stimulation time-dependent manner. The EGF phase-response curve differed from that of forskolin (FK)—a well-known chemical resetting stimulus—both in the advance/delay ratio and stimulation time-dependency. PCR array analysis followed by quantitative PCR validation demonstrated that EGF treatment transiently induced multiple clock-related genes including Per1, Per2, Dec1, e4bp4, and Noct, whereas FK treatment induced a limited number of genes (Per1 and Dec1), suggesting that the mode of entrainment of NSC molecular clock was different for EGF and FK. EGF led to gene induction in the presence of cycloheximide, suggesting that de novo protein synthesis is unnecessary. Pretreatment with the MEK1/2 inhibitor U0126 significantly suppressed the acute induction of Per2, Dec1, and Noct by EGF and also abolished the EGF-induced phase shift of the PER2::LUCIFERASE rhythm in NSCs. These results suggest a unique effect of EGF on the molecular clockwork of NSCs.

Incipient motion of a non-cohesive particle under Stokes flow conditions

Erosion and deposition of sediments in the presence of shearing flows are two phenomena commonly encountered in natural, biological and industrial processes. In determining the critical conditions for the initiation of motion (onset of erosion), a force-magnitude approach has been historically used by employing either the time-averaged or the instantaneous peak fluctuating forces exerted on the sediment particles. Such approach however, has been proven to be incapable of uniquely determining the onset of sediment motion under rapidly fluctuating forces and thus alternative formulations, including impulse- and energy-based methods, have been proposed for turbulent flow conditions. Nevertheless, the force-magnitude approach, can still be applied in the case of very slow viscous flows (Stokes regime) when non-cohesive particles are considered. In the present study, we consider the problem of initiation of motion of a single mobile particle resting on a surface populated by similar types of grains and being exposed to a linear shear flow. The hydrodynamic forces and torques are computed numerically by considering Stokes flow conditions and solving the governing equations using the boundary element method (BEM). To further simplify our model, the bed substrate is parametrised by a flat wall while the pocket shielding effects are taken into account by shifting the linear shear flow towards the fluid. Subsequently, the critical conditions are uniquely determined by applying a force magnitude-based approach and considering rolling and sliding to be the possible modes of entrainment. The computed critical Shields numbers are compared to existing experimental data from the literature showing a very good overall agreement. Finally, the differences and similarities between the two extreme regimes, Stokes flow and fully rough turbulent flow threshold conditions, are briefly discussed.

Noise Induces Hopping between NF-κB Entrainment Modes

SUMMARYOscillations and noise drive many processes in biology, but how both affect the activity of the transcription factor nuclear factor κB (NF-κB) is not understood. Here, we observe that when NF-κB oscillations are entrained by periodic tumor necrosis factor (TNF) inputs in experiments, NF-κB exhibits jumps between frequency modes, a phenomenon we call “cellular mode-hopping.” By comparing stochastic simulations of NF-κB oscillations to deterministic simulations conducted inside and outside the chaotic regime of parameter space, we show that noise facilitates mode-hopping in all regimes. However, when the deterministic system is driven by chaotic dynamics, hops between modes are erratic and short-lived, whereas in experiments, the system spends several periods in one entrainment mode before hopping and rarely visits more than two modes. The experimental behavior matches our simulations of noise-induced mode-hopping outside the chaotic regime. We suggest that mode-hopping is a mechanism by which different NF-κB-dependent genes under frequency control can be expressed at different times.

Complex Patterns of Metabolic and Ca2+ Entrainment in Pancreatic Islets by Oscillatory Glucose

Glucose-stimulated insulin secretion is pulsatile and driven by intrinsic oscillations in metabolism, electrical activity, and Ca2+ in pancreatic islets. Periodic variations in glucose can entrain islet Ca2+ and insulin secretion, possibly promoting interislet synchronization. Here, we used fluorescence microscopy to demonstrate that glucose oscillations can induce distinct 1:1 and 1:2 entrainment of oscillations (one and two oscillations for each period of exogenous stimulus, respectively) in islet Ca2+, NAD(P)H, and mitochondrial membrane potential. To our knowledge, this is the first demonstration of metabolic entrainment in islets, and we found that entrainment of metabolic oscillations requires voltage-gated Ca2+ influx. We identified diverse patterns of 1:2 entrainment and showed that islet synchronization during entrainment involves adjustments of both oscillatory phase and period. All experimental findings could be recapitulated by our recently developed mathematical model, and simulations suggested that interislet variability in 1:2 entrainment patterns reflects differences in their glucose sensitivity. Finally, our simulations and recordings showed that a heterogeneous group of islets synchronized during 1:2 entrainment, resulting in a clear oscillatory response from the collective. In summary, we demonstrate that oscillatory glucose can induce complex modes of entrainment of metabolically driven oscillations in islets, and provide additional support for the notion that entrainment promotes interislet synchrony in the pancreas.

Experimental study of air entrainment mode with natural ventilation using shafts in road tunnel fires

A set of burning experiments with n-heptane pool fire were conducted to investigate the air entrainment mode with natural ventilation using shafts in road tunnel fires. One criterion was proposed to determine the critical shaft height of the plug-holing occurrence in our previous work whereas this study quantificationally analyzes the effect of plug-holing on the smoke exhaust efficiency. The disturbance of smoke exhausting on the smoke–air interface, which causes different amounts of fresh air exhausted directly and indirectly, is investigated. Results show that using vertical shafts to discharge smoke leads to a strong mixing process between the smoke layer and the fresh air. Consequently, about 2/3 of the smoke exhausting rate of the shaft is air. Moreover, some of the entrained air mixes into the smoke layer downstream the shaft, resulting, in a small reduction amount of the spilling smoke, which also proves an inefficient smoke exhausting process. Hence, for the sake of improving effectiveness of natural ventilation, some significant improvements are needed in practice.

Role of instantaneous force magnitude and duration on particle entrainment

A new criterion for the onset of entrainment of coarse sediment grains is presented here. It is hypothesized that not only the magnitude, but also the duration of energetic near bed turbulent events is relevant in predicting grain removal from the bed surface. It is therefore proposed that the product of force and its duration, or impulse, is a more appropriate and universal criterion for identifying conditions for particle dislodgement. This conjecture is investigated utilizing two theoretical models, representative of two modes of entrainment: saltation and rolling. In these models, instantaneous, highly fluctuating turbulent forces are simulated as short‐lived pulses of characteristic magnitude and duration, which transfer adequate fluid momentum to the particle, to trigger its entrainment. The analytical solution of the respective equations of motion is employed in deriving representations of threshold conditions in terms of the impulse characteristics. It is shown that hydrodynamic forces of sufficiently high magnitude are capable of entraining a particle only when they last long enough so that their impulse exceeds a critical value. To illustrate further the validity of the critical impulse concept, as well as extend and generalize its application to different entrainment levels of an individual grain, a novel experimental setup is utilized. This setup facilitates observations of angular displacement of a steel mobile particle in air due to electromagnetic pulses of different magnitude and duration. The experimentally obtained conditions for partial or complete entrainment support the concept of a critical impulse.

Wavelike gas dispersion in a liquid in a compressor-free environment

An experimental investigation has been performed regarding the operation of a new type of wave-generating gas disperser in a liquid in entrainment mode in a compressor-free environment. The wave-generating disperser and ejector-caused gas flow relationship with the water pressure at the disperser inlet under different design factors has been obtained. The gas bubbles’ average size has been measured in a biphase stream leaving the disperser. Recommendations for the selection of the disperser parameters have been submitted. The goal of this work is the simplification of plants intended for dispersing gas in a liquid, diminishing the gas bubbles’ size, and reducing the dispersion energy flow. This is a pressing problem for many chemical technology targets, for wastewater biological treatment systems, and for chlorinating or ozonizing tap water.

Experimental study of the effects of a thermal plume entrainment mode on the flow structure: Application to fire

The aim of this work is to experimentally simulate two heat sources of fire, one placed at ground level, the other at a height above the ground, in order to determine the effect of source air entrainment on the resulting flow structure. The development of a free thermal plume was examined by generating a plume produced from an electrically heated disk at a constant temperature. We first studied the behavior of a thermal plume induced by a disk embedded in a horizontal plate placed at the level of the ground. This configuration ensured a regular lateral entrainment of air to the plume. The analysis of the average fields as well as the axial evolution of velocity and temperature showed an important widening of the profiles that encouraged a faster spread of the plume. We then determined the structure of the thermal plume generated by the same source placed at a height above the ground, ensuring simultaneous vertical and lateral entrainment of air into the resulting plume. Results obtained reveal a vertical elongation of the average profiles that limits the lateral extension of the plume flow. Comparison of the plumes produced from the two configurations showed that the flow structure is strongly influenced by the nature of the source of air entrainment. An additional vertical contribution of air entrainment caused the location of the maximum axial velocity above the source to be raised, with the flow rate and the thermal flux absorbed by the air experiencing a relative increase of the order of 14% and 34%, respectively.

Field experiments and numerical modeling of mass entrainment in snow avalanches

Snow entrainment alters the speed and hence the run‐out distance of avalanches, yet little is known about this significant process. We studied entrainment in snow avalanches using observations from (1) the Swiss Vallée de la Sionne test site, (2) the Italian Pizzac site, (3) catastrophic avalanches that occurred during the winter 1998–1999 in Switzerland, and (4) a medium‐sized spontaneous avalanche that occurred in 2000 in Davos, Switzerland. We determined mass and energy balances for 18 avalanche events. On average, the mass increased by a factor of 4. The primary mode of entrainment appeared to be frontal ploughing, although entrainment behind the avalanche front was also observed. Step entrainment, where a snow cover layer fractures and is entirely consumed by the avalanche, also occurred. Basal erosion was negligible. Mass availability and snow cover structure were the limiting factors governing entrainment. Other factors such as track topography and avalanche dimension played a secondary role. Using the experimental results, we introduced an entrainment model into a Saint‐Venant type flow model where the internal shear deformation of the avalanche is governed by a Bagnold law and the shear stress at the basal layer is treated as a Voellmy fluid. The model with entrainment not only improves the prediction of the velocities and flow heights in comparison to measurements, but also reproduces the variations in run‐out distances, which characterize avalanches with similar terminal velocities but different masses.

Processes driving the episodic flux of faecal indicator organisms in streams impacting on recreational and shellfish harvesting waters

Understanding the process controls on episodic fluxes of faecal indicator organisms (FIOs) is becoming increasingly important for the sustainable management and accurate modelling of water quality in both recreational and shellfish harvesting waters. Both environments exhibit transitory non-compliance with microbiological standards after rainfall episodes despite significant expenditures on control of sewage derived pollutant loadings in recent years. This paper demonstrates the role of wave propagation in the entrainment of FIOs from river channel beds as a contributor to episodes of poor microbial water quality. Previously reported data is reviewed in the light of relationships between wave and mean water travel velocities. High flows and rapid changes in river flow, driven by releases of bacterially pure reservoir water, resulted in elevated FIO concentrations and transient peaks in concentration. The new interpretation of these data suggest three modes of entrainment: (i) immediate wave-front disturbance, (ii) wave propagation lift and post-wave transport at mean flow velocity, and (iii) stochastic erosional mechanisms that maintain elevated bacterial concentrations under steady high flow conditions. This is a significant advance on the previously proposed mechanisms. Understanding these mechanisms provides an aid to managing streams intended for recreational use and emphasises the need to control the timing of high flow generation prior to use of the water body for e.g. canoeing events. In addition the processes highlighted have relevance for the protection of shellfish nurseries, drinking water supply intakes and episodes of poor bathing water quality, and associated health risks.

A phase response curve for circannual rhythm in the varied carpet beetle Anthrenus verbasci

We know that entrainment, a stable phase relationship with an environmental cycle, must be established for a biological clock to function properly. Phase response curves (PRCs), which are plots of phase shifts that result as a function of the phase of a stimulus, have been created to examine the mode of entrainment. In circadian rhythms, single-light pulse PRCs have been obtained by giving a light pulse to various phases of a free-running rhythm under continuous darkness. This successfully explains the entrainment to light-dark cycles. Some organisms show circannual rhythms. In some of these, changes in photoperiod entrain the circannual rhythms. However, no single-pulse PRCs have been created. Here we show the PRC to a long-day pulse superimposed for 4 weeks over constant short days in the circannual pupation rhythm in the varied carpet beetle Anthrenus verbasci. Because the shape of that PRC closely resembles that of the Type 0 PRC with large phase shifts in circadian rhythms, we suggest that an oscillator having a common feature in the phase response with the circadian clock, produces a circannual rhythm.