Frequency Demultiplication Research Articles

The circadian clock of the bacterium B. subtilis evokes properties of complex, multicellular circadian systems.

Circadian clocks are pervasive throughout nature, yet only recently has this adaptive regulatory program been described in nonphotosynthetic bacteria. Here, we describe an inherent complexity in the Bacillus subtilis circadian clock. We find that B. subtilis entrains to blue and red light and that circadian entrainment is separable from masking through fluence titration and frequency demultiplication protocols. We identify circadian rhythmicity in constant light, consistent with the Aschoff's rule, and entrainment aftereffects, both of which are properties described for eukaryotic circadian clocks. We report that circadian rhythms occur in wild isolates of this prokaryote, thus establishing them as a general property of this species, and that its circadian system responds to the environment in a complex fashion that is consistent with multicellular eukaryotic circadian systems.

Van der Pol oscillator based on NbO2 volatile memristor: A simulation analysis

Nature positively embodies a rich yet complex array of nonlinear phenomena. To date, it has remained unclear how to exploit these phenomena to solve a wide range of problems. The Van der Pol oscillator is one of the nonlinear dynamical systems that hold tremendous promise for a broad range of important applications from a circuit performance booster to hard problem solving to mapping the biological nonlinear dynamics. Here, we theoretically build a Van der Pol oscillator circuit using a NbO2 volatile memristor to perform a systematic analysis of the complex nonlinear dynamic behavior. Three types of oscillation phenomena including period doubling, quasi-period, and chaos are obtained by varying the parallel capacitance and futher distinguished by mathematical analysis, such as fast Fourier transform, Poincaré plots, and plane trajectories of voltage on the memristor. The frequency locking phenomenon of the system is presented to enable a programmable frequency demultiplication. Moreover, the other critical circuit parameters such as DC voltage amplitude, load resistance, and AC driving frequency are also modulated to understand the nonlinear dynamic behavior of the system. All these analyses provide a viable platform to understand and implement nonlinear systems for a broad range of multifunctional oscillatory devices.

Principles underlying the complex dynamics of temperature entrainment by a circadian clock

SummaryAutonomously oscillating circadian clocks resonate with daily environmental (zeitgeber) rhythms to organize physiology around the solar day. Although entrainment properties and mechanisms have been studied widely and in great detail for light-dark cycles, entrainment to daily temperature rhythms remains poorly understood despite that they are potent zeitgebers. Here we investigate the entrainment of the chronobiological model organism Neurospora crassa, subject to thermocycles of different periods and fractions of warm versus cold phases, mimicking seasonal variations. Depending on the properties of these thermocycles, regularly entrained rhythms, period-doubling (frequency demultiplication) but also irregular aperiodic behavior occurs. We demonstrate that the complex nonlinear phenomena of experimentally observed entrainment dynamics can be understood by molecular mathematical modeling.

Quantitative evaluation of morphological characteristics of thin sand body: Taking the deltaic distributary channel sand body as an example in Shengtuo oil field of Dongying sag, east of Bohai Bay Basin

Because of the small scale of distributary channel sand body and the superposition of sand bodies in vertical and lateral direction, drilling data with 150–200 m well spacing is difficult to describe its scale, shape and connectivity characteristics effectively. It has a great restriction on the recovery of these reservoirs. Taking Sheng2 Block of Shengtuo Oilfield as an example, the architectural elements of distributary channel are quantitatively investigated by using dense-drilling well and seismic data. Based on frequency division seismic data, the boundary of distributary channel belts are described vertically and laterally, and then the scale and morphological characteristics of channel bodies in the channel belt are characterized by using local dense well pattern data. The target layer can be divided into six channel belts longitudinally. After seismic frequency demultiplication, 60–75 Hz seismic data was used to describe the distribution of channel belts. From the bottom to the top, the width and distribution range of the channel belts decrease as a whole. Channel belt thickness and its width show linear positive correlation. On the channel-belt cross section, channel stories on the dense drilling-well logging profiles are identified with reference to the profile geometry of the distributary channel. On the channel-belt cross section, the projection distance between wells is fitted to a linear correlation with the thickness variation of channel stories. The ratio of the two parameters decreases from bottom to top of the target layer as a whole. The channel shape parameters predicted by the dense drilling-well logging section are of great significance to the study of paleocurrent deposition and paleohydrological evolution. At the same time, it has guiding significance for the development and adjustment of oil and gas reservoirs.

Investigation on the effect of vibration frequency on vortex-induced vibrations by section model tests

Higher-mode vertical vortex-induced vibrations (VIV) have been observed on several steel box-girder suspension bridges where different vertical modes are selectively excited in turn with wind velocity in accordance with the Strouhal law. Understanding the relationship of VIV amplitudes for different modes of vibration is very important for wind-resistant design of long-span box-girder suspension bridges. In this study, the basic rectangular cross-section with side ratio of B/D=6 is used to investigate the effect of different modes on VIV amplitudes by section model tests. The section model is flexibly mounted in wind tunnel with a variety of spring constants for simulating different modes of vibration and the non-dimensional vertical amplitudes are determined as a function of reduced velocity U/fD. Two 'lock-in' ranges are observed at the same onset reduced velocities of approximately 4.8 and 9.4 for all cases. The second 'lock-in' range, which is induced by the conventional vortex shedding, consistently gives larger responses than the first one and the Sc-normalized maximum non-dimensional responses are almost the same for different spring constants. The first 'lock-in' range where the vibration frequency is approximately two times the vortex shedding frequency is probably a result of super-harmonic resonance or the "frequency demultiplication". The main conclusion drawn from the section model study, central to the higher-mode VIV of suspension bridges, is that the VIV amplitude for different modes is the same provided that the Sc number for these modes is identical.

Error Analysis and Improvement of Equal Precision Frequency Measurement

In accordance with the principle of equal precision frequency measurement and theory of errors, in this paper, the problems are discussed that the equal precision frequency measurement eliminates the standard frequency count error. In order to reduce the relative error and improve the measurement accuracy, a method is proposed for phase coincide detection between standard frequency multiplication and measurement frequency demultiplication to open or shut the gate, at the same time, a signal selector is also used to improve circuit performance. This method can effectively solve the problem that the frequency can not be detected without the synchronization signal and improve the performance of the frequency measurement system.

Counting Circadian Cycles to Determine the Period of a Circasemilunar Rhythm in a Marine Insect

Semilunar and lunar rhythms are often controlled endogenously, but the mechanisms of their respective free-run periods, when external factors are absent, are mostly unclear. In this investigation, the authors studied the mechanism controlling the period of the circasemilunar emergence rhythm of a marine midge, Pontomyia oceana, in southern Taiwan. Experimental approaches were adopted with various artificial light-dark (LD) periods, or T, from 22 to 28 h per cycle in the first experiment, and 18 to 30 h per cycle in the second experiment, as treatments on the same cohorts of midge larvae. The responses in emergence days were directly proportional to the magnitude of the treatments, just as that predicted by the frequency demultiplication hypothesis. A counting mechanism is thus the only hypothesis supported by this finding. To further test whether it is endogenous oscillations that are counted, submultiples as well as multiples of 24 h, i.e., 6, 12, 24, and 48 h per cycle, were used as T. The midges under all these treatments emerged at similar days. This result supports the hypothesis that endogenous circadian oscillations, not external LD cycles, are counted in this circasemilunar emergence rhythm of the marine midge. This paper reports a first case supporting the frequency demultiplication hypothesis in a circasemilunar rhythm that is based on counting the cycles of endogenous circadian rhythms. (Author correspondence: keryea@mail.nsysu.edu.tw)

High-Precision Timing System Based on Microcontroller

The task of timing system is countdown on a set date and showing the time from current date to the setting date to enhance people’s attention and sense of urgency. A kind of high-precision timing system is introduced. The system is controlled by single-chip microcontroller. High integration clock chip is used as clock module. System hardware design and software design are introduced. System hardware design includes design of clock module, its connection with single-chip microcomputer, and the design of display module. System software design includes the settings of single-chip serial port, its initialization, the reading and writing of the clock module, the countdown program and the display program. Compared with other timing system which consists of frequency demultiplication by multivibrator, this system is more stable and reliable. The accumulative error is zero when long-time running continuously. Because the system control module is simple, it is convenient to be developed and utilized. Practice shows that this high-precision timing system can meet practical needs well.

Nonlinear Analysis Based on Experiments of the Rotation Shaft System of Mine Drainage Motor and Pump

The experimental study results show that the system’s nonlinear characteristics, incluing the dynamic responses of the poincare mapping, the bifurcation plots, three-dimensional waterfalls diagrams etc. The effects factors of system experiment are studied and analyzed, including the misalignment and the rub-impact stiffness on system responses. So, the faults characteristics of the misalignment and the rub-impact of the rotation shaft-mechanical seal system on the drainge motor and drainge pump are also gained by the experiment. The dynamic performance of the system show nonlinear characteristics in different working conditions. The rotating shaft-mechanical seal system on the drainge motor and drainge pump can be optimization design and performance prediction based on the studied results of our work. The experiment’s results show that: the multiple frequencies are produced of the rotating shaft-mechanical seal system on drainge motor and drainge pump, and the frequencies of 1-time and 2-time are dominating components under the exciting force effects of misalignment and imbalance. At the fault state of misalignment coupling rub-impact, the multiple frequencies including 2-time, 3-time, 4-time and so on, will be induced under the critical speed. Over the value of the critical speed, will cause the phenomenon of frequency demultiplication and chaos. With rub-impact stiffness value increased, the phenomenon of frequency demultiplication and chaos are induced more frequently; with the degree of misalignment increased, the phenomena of chaos will decrease and the system will tend to be the stable state.

Daily activity patterns of a nocturnal and a diurnal rodent in a seminatural environment

The entrainment of circadian rhythms by light–dark (LD) cycles has been extensively investigated in laboratory studies. In almost all of these studies, organisms have not been allowed to modulate their exposure to the LD cycle. In the present study, the rhythm of running-wheel activity was investigated in nocturnal (domestic mice) and diurnal (Nile grass rats) rodents provided with light-tight nest boxes and maintained under long and short photoperiods. Photoperiod length had a significant effect on the duration of the daily active phase ( α), on the phase angle of entrainment ( Ψ), and on diurnality or nocturnality in both species. The availability of a nest box had a modest effect only on the variability of activity onsets. Neither in the nocturnal nor in the diurnal species was there any evidence of entrainment by frequency demultiplication or of entrainment without photic stimulation at either dawn or dusk. These results indicate that at least in the species studied, the ability of rodents to modulate their exposure to the LD cycle does not have a major effect on photic entrainment.

Evaluation of the Frequency Demultiplication Hypothesis of Circannual Pupation Rhythm in the Varied Carpet Beetle Anthrenus verbasci (Coleoptera: Dermestidae)

The present study was reported to examine whether the circannual pupation rhythm in Anthrenus verbasci is derived from a circadian rhythm through a process of frequency demultiplication. This frequency demultiplication hypothesis requires that the period of the circannual rhythm is proportional to the period of the entrained circadian rhythm. When larvae were reared under constant photoperiods of T = 20h, 22h, 24h and 26h at 20°C, the larval duration differed among the photoperiodic conditions, although there was no positive correlation between the period of T cycle and larval duration. The differences among photoperiods may have been caused by the duration of the photophase. Therefore, the results did not support the frequency demultiplication hypothesis.

On the diffraction of autowaves

The paper is concerned with the passage of autowaves through one or two holes in an impermeable screen, their diffraction at a screen edge, and their passage through narrow channels in a thick screen. The following interesting phenomena were observed: aperiodicity in wave trains behind the screen (chaos) and frequency demultiplication in the case of a periodic train of autowaves incident on a narrow hole in an impermeable screen; the effect of autowave reflection from a hole; the possibility for a narrow channel to become a source of periodic autowaves. The studies were performed by numerical experiments with a model of an excitable medium of the FitzHugh-Nagumo type.

Subharmonic entrainment of a forced relaxation oscillator

Using a simplified model of a relaxation oscillator which exhibits the characteristic free response of intervals of slow decay separated by rapid jumps, we determine steady-state response to a harmonic forcing input and obtain regions in the parameter space where subharmonic entrainment occurs. The model relaxation oscillator consists of a one-dimensional flow with jump conditions and is motivated by earlier studies of the flow on the slow manifold of a piecewiselinear relaxation oscillator. The results are obtained by studying the dynamics of the phase mapping which describes how the forcing phase varies between jumps. Details of the phase mapping are obtained both analytically and by numerical integration of the governing flow. The results obtained regarding existence and stability of subharmonics bear strong qualitative resemblance to experimental observations of frequency demultiplication by van der Pol and van der Mark (1927) and to numerical investigations of the forced van der Pol oscillator by Flaherty and Hoppensteadt (1978).

Circannual Rhythms of Ground Squirrels: A Test of the Frequency Demultiplication Hypothesis

The frequency demultiplication hypothesis (FDH) posits that circannual rhythms are generated from circadian cycles by frequency transformation to the lower-frequency rhythm. To test the FDH, we determined the periods of the circannual body mass and estrous cycles of golden-mantled ground squirrels with circadian locomotor activity rhythms entrained to 23-, 24-, or 25-hr days (T-cycles). Circannual period length did not differ among squirrels entrained to the different T-cycles; intergroup ranges were 298-314 days and 303-312 days, respectively, for body mass and estrus. These results are not consistent with the FDH and suggest instead that separate mechanisms generate circadian and circannual rhythms. In ground squirrels the circannual system influences circadian organization, but a reciprocal influence of circadian on circannual rhythms has yet to be demonstrated.

Circadian organization in cockroaches: Effects of temperature cycles on locomotor activity

The effects of various temperature cycles on the locomotor activity of the cockroach Leucophaea maderae were investigated. While bilateral ablation of the optic lobes abolished the free-running activity rhythm in constant conditions, rhythmicity was exhibited by lobeless animals placed in temperature cycles. The rhythms were driven by cycles as short as 12 h and as long as 48 h without evidence of frequency division or frequency demultiplication. The phase relationship between activity onset and the temperature cycle was dependent on both the relative durations of the “warm” and “cold” phases of the cycles and on the period of the cycle. Computer simulations indicated that these properties of the rhythm can be explained by proposing that activity is controlled by a damped oscillator, located outside the optic lobes, that can be forced by cycles of temperature.

The effect of light regimes on the circadian rhythm of flight activity in the mosquito Aedes taeniorhynchus.

ABSTRACT The flight activity patterns of groups and individuals of sugar-fed A. taeniorhynchus females have been studied under different light regimes, by recording of flight sound as an indicator of flight activity. In an LD 12:12 regime, flight activity occurs both at light-off and light-on, forming a bimodal ‘alternans’ pattern. This basic pattern of flight activity persists with a periodicity of 23.5 h under continuous DD, but under continuous LL is masked over by irregular excessive outbursts of activity. The flight activity rhythm originates for the first time in the adult stage, and it is not carried over from rhythms of developmental stages. Flight activity rhythms can be entrained to a new light regime within 24 –36 h which is rather fast. An early light-off does not reset the phase of the rhythm, but a delayed light-off does. The flight activity rhythm can be entrained to 24 h light regimes other than LD 12:12. But a single stimulus of less than 12 h is not effective in initiating the bimodal circadian rhythm. Frequency demultiplication within certain limits can entrain the flight activity rhythm to 24 h. This flight activity rhythm of A. taeniorhynchus is compared with the activity rhythms of Aopheles gambiae and Culex pipiens pallens. It is concluded that the basic bimodal alternans pattern of flight activity is a persistent property of the circadian oscillating system, which suggests that other activity rhythms involving flight are dependent on the same rhythm.

The occurrence of an endogenous circadian rhythm in a plant tissue culture.

Leaves of the succulent plants Bryophyllumn, fedtschenkoi and B. daigremnontianutni, show an endogenous circadian rhythm in their rate of CO., metabolism (9, 10, 11, 12). The extent to which the occurrence of the rhythm depends upon the organization of the leaf has been investigated with callus cultures of Bryophyllumi. leaf tissue. There has been but one previous report of a persistent rhythm in a plant tissue culture. Enderle (3) observed rhythmic fluctuations in growth and turgidity of cultures of Daucus carota and found the rhythmicity to persist in prolonged darkness. Investigation of the rhythm necessarily involved microscopic examination of the cultures and this was done with red light at intervals of approximately 4 hours. Since red light is particularly active in affecting plant rhythms (4, 5, 7, 11), and some organisms (e.g. Euglena) are known to have the capacity for frequency demultiplication (1, 2), the diurnal periodicity in growth and turgidity might have arisen from the periodic stimulation with red light. Enderle (3) does not appear to have established whether or not the phase of the rhythm can be set at different times of day. Unequivocal evidence of the occurrence of endogenous rhythms in plant tissue cultures is therefore lacking. The endogenous nature of rhythmicity in animal tissue cultures (6, 8) has also yet to be firmly established.

An endogenous rhythm in the rate of carbon dioxide output of Bryophyllum. IV. Effect of intensity of illumination on entrainment of the rhythm by cycles of light & darkness

Excised leaves of the succulent plant Bryophyllum fedtschenkoi show an endogenous circadian rhythm in their rate of carbon dioxide emission (17,18). The rhythm occurs when leaves kept at a constant temperature and in an air stream initially free from carbon dioxide are transferred from light to prolonged darkness. The of the basic oscillating system in Bryophyllum leaf cells by various cycles of light and darkness and the extent to which depends upon the light intensity in the cycles are described in this paper. Exposure of an organism to cycles other than 24 hours in length can modify the period of its endogenous circadian rhythm. When this occurs the period usually becomes either equal to, or a multiple of, that of the stimulating cycles. The former phenomenon is termed entrainment and the latter is a special type of known as frequency demultiplication. Both plant and animal rhythms can be entrained by cycles of light and darkness having a period other than 24 hours. In most organisms such occurs only when the amount by which the period differs from 24 hours lies within certain limits, and these appear to be different in different organisms. When the period of the light-dark cycles is less than 24 hours, clearly defined limits of have been observed in all organisms investigated. For example, the rhythm of leaf movement in Canavalia ensiformis entrains to 8: 8 but not to 6: 6 hour cycles of light and darkness (8), whereas that of petal movement in Kalanchoe blossfeldiana entrains to 6: 6 but not to 4: 4 hour cycles (5). On the other hand, when the period of the stimulating cycles exceeds 24 hours limits of have been observed in a few organisms (2, 4, 12) but not in others (8,9, 10, 14, 15). Entrainment data for plant and animal rhythms have recently been tabulated and discussed by Bruce (1). Although the limits of have been determined for a number of biological oscillating systems and given considerable emphasis in the literature (1, 3), the extent to which they are a function of the light intensity in the stimulating cycles has not previously been critically investigated. Furthermore, little attention has been given to the possibility that the observed is the result only of a direct effect of light on the biochemical or physiological process being used to monitor the behavior of the unidentified basic oscillating systems.

A New Method of Speech Transmission by Frequency Demultiplication and Multiplication

A New Method of Speech Transmission by Frequency Demultiplication and Multiplication

Oscillations in Certain Nonlinear Driven Systems

The development of the theory of nonlinear oscillating systems has given rise to some rather intractable nonlinear differential equations. The formerly used isoclyne method of solution is inadequate for the solution of the equation of the nonlinear system producing relaxation oscillations under the influence of an impressed periodic force. In this paper, using the specific example of a triode oscillator with impressed sinusoidal electromotive force, differential analyzer solutions of the governing diferential equation, are given. A brief study of the phenomena of automatic synchronization and frequency demultiplication is made on the basis of the nonlinear theory.