Dora Pancheva - Academia.edu (original) (raw)

Papers by Dora Pancheva

Research paper thumbnail of Vertical coupling in the atmosphere/ionosphere system - Preface

Journal of Atmospheric and Solar-Terrestrial Physics

Research paper thumbnail of Model of the electron density height profile in the lowest D-region (50 to 75 km)

Advances in Space Research, 1995

Research paper thumbnail of Planetary wave coupling of the atmosphere–ionosphere system during the Northern winter of 2008/2009

Advances in Space Research, 2012

ABSTRACT This paper presents the global spatial (latitude and altitude) structure and temporal va... more ABSTRACT This paper presents the global spatial (latitude and altitude) structure and temporal variability of the ∼23-day ionospheric zonally symmetric (s = 0) planetary wave (PW) seen in the Northern winter of 2008/2009 (October 2008–March 2009). It is shown that these ∼23-day ionospheric oscillations are forced from PWs propagating from below. The COSMIC ionospheric parameters foF2 and hmF2 and electron density at fixed altitudes and the SABER temperatures were utilized in order to define the waves which are present simultaneously in the atmosphere and ionosphere. The long-period PWs from the two data sets have been extracted through the same data analysis method. The similarity between the lower thermospheric ∼23-day (s = 0) temperature PW and its ionospheric electron density response provides valuable and strong experimental evidence for confirming the paradigm of atmosphere–ionosphere coupling.

Research paper thumbnail of Global-scale tidal variability during the PSMOS campaign of June–August 1999: interaction with planetary waves

Journal of atmospheric and solar-terrestrial physics, Nov 30, 2002

During the PSMOS Global-scale tidal variability experiment campaign of June 1–August 31, 1999, a ... more During the PSMOS Global-scale tidal variability experiment campaign of June 1–August 31, 1999, a network of radars made measurements of winds, waves and tides in the mesosphere/lower-thermosphere region over a wide range of latitudes. Clear evidence was found that fluctuations in tidal amplitudes occur on a global scale in both hemispheres, and that at least some of these fluctuations are periodic in nature. Modulation of the amplitude of the 12 h tide was particularly evident at periods of 10 and 16 days, suggesting a non- ...

Research paper thumbnail of Global-scale tidal structure in the mesosphere and lower thermosphere during the PSMOS campaign of June–August 1999 and comparisons with the global-scale wave model

Journal of atmospheric and solar-terrestrial physics, May 7, 2002

Observations of mean winds and semidiurnal and diurnal tides in the mesosphere/lower-thermosphere... more Observations of mean winds and semidiurnal and diurnal tides in the mesosphere/lower-thermosphere (MLT) region were made during the 3-month Planetary-Scale Mesopause Observing System Summer 1999 campaign. Data from 22 ground-based radars (and from two other instruments with measurements for the same period but in 1998) allow us to investigate the ability of the GSWM-00 to simulate the solar tides in the mesopause region (90–95 km). Here we have found that the GSWM-00 provides an increasingly reasonable ...

Research paper thumbnail of Long-term prediction of the foF2 on the rising and falling parts of the solar cycle

Advances in Space Research, 1994

In this paper we intend to enlarge the fof2 long-term prediction accuracy taking into account the... more In this paper we intend to enlarge the fof2 long-term prediction accuracy taking into account the systematic variations of the hysteresis and secular-time phenomena.

Research paper thumbnail of Mesosphere/lower thermosphere prevailing wind model

Advances in Space Research, 2004

... r Physics and Maths Physics, University of Adelaide, Adelaide 5005, Australia. s INPE Aeronom... more ... r Physics and Maths Physics, University of Adelaide, Adelaide 5005, Australia. s INPE Aeronomy Division, CP 515, Sao Jose dos Campos, SP 12200, Brazil. t Department of Physics and Electronics, Rhodes University, PO Box 94, Grahamstown 6140, Republic of SouthAfrica. ...

Research paper thumbnail of Quasi-periodic fluctuations in ionospheric absorption in relation to planetary activity in the stratosphere

Journal of atmospheric and …, 1991

Quasi-periodic fluctuations (2-15 days) in ionospheric absorption along three radio paths in Cent... more Quasi-periodic fluctuations (2-15 days) in ionospheric absorption along three radio paths in Central and Southern Europe are investigated for three winter periods 1985/86, 1986/87 and 1987/88. The periods of dominant fluctuations in absorption and the time variations of their amplitudes are similar for all radio paths and every winter period. The shorter-period fluctuations are found to be associated with enhancements of planetary wave two activity in the stratosphere (30 hPa, 60"N), while longer period fluctuations appear to be associated with intensification of planetary wave one activity in the stratosphere.

Research paper thumbnail of Planetary waves and midlatitude sporadic E layers: Strong experimental evidence for a close relationship

J. Geophys. Res, 2002

Dora Pancheva Department of Physics, University of Wales, Aberystwyth, Wales, UK Received 17 July... more Dora Pancheva Department of Physics, University of Wales, Aberystwyth, Wales, UK Received 17 July 2001; revised 24 September 2001; accepted 28 September 2001; published 19 June 2002. [1] A large-amplitude, 7-day period westward propagating S = 1 planetary wave ...

Research paper thumbnail of Planetary wave activity in the lower ionosphere during CRISTA I campaign in autumn 1994 (October-November)

Annales Geophysicae, 1998

On the basis of MEM spectrum analysis, the main planetary scale¯uctuations formed in the lower io... more On the basis of MEM spectrum analysis, the main planetary scale¯uctuations formed in the lower ionosphere are studied over a period of 3±25 days during the CRISTA campaign (October-November 1994). Three dominant period bands are found: 3±5, 6±8 and 15±23 (mainly 16±18) days. For 7±8 and 16±18 daȳ uctuations, propagation was eastward with wave numbers K = 3 and K = 1, respectively. The magnitude of planetary wave activity in the mid-latitudes of the Northern Hemisphere during the CRISTA campaign seems to be fairly consistent with the expected undisturbed normal/climatological state of the atmosphere at altitudes of 80±100 km.

Research paper thumbnail of Non-linear interaction of tides and planetary waves in the mesosphere and lower thermosphere: observations over Europe

Physics and Chemistry of the Earth, Part C: Solar, Terrestrial & Planetary Science

ABSTRACT

Research paper thumbnail of Global Empirical Model of the TEC Response to Geomagnetic Activity and Forcing from Below

Research paper thumbnail of Influence of Solar Activity on the Summer Electron Density Profiles in Thelower Midlatitude D-Region

Dokladi Na B Lgarskata Akademiâ Na Naukite, 1998

Research paper thumbnail of Quasiperiodic oscillations in the ionospheric absorption of solar and inner-atmospheric origin

A band-pass filter is used to study two aspects of a wave response in the lower ionosphere with a... more A band-pass filter is used to study two aspects of a wave response in the lower ionosphere with a period close to that of the solar rotation period. This response was brought about by both short-period (about 27 d) oscillations of solar activity and waves generated inside the atmosphere itself. In the first instance, the fluctuations generated in the D-region ionosphere (80-95 km) are synchronous with the 27-day oscillations, and in the lower D-region (from the base of the ionosphere to about 75 km) there is no noticeable reaction. A strong wave reaction is observed in the wintertime upper and lower D-region of the ionosphere when the 27-day oscillations are close to nonexistent. The wave reaction has a period of 24-28 days and consists of waves generated inside the atmosphere itself and propagating vertically upward. On average, the fluctuation amplitude in the field of the ionospheric absorption increases with height. The average period also changes with height; for the lower D-region it consists of 24-25 days, while for the upper region it is 26-27 days.

Research paper thumbnail of Tidal variability during stratospheric sudden warming in 2009: Comparison between GAIA model and COSMIC and TIMED/SABER observations

ABSTRACT We compare results from a whole atmosphere-ionosphere coupled model, GAIA, and from the ... more ABSTRACT We compare results from a whole atmosphere-ionosphere coupled model, GAIA, and from the COSMIC and TIMED/SABER observations during 2008/2009 northern winter season. The GAIA model has assimilated meteorological reanalysis data by a nudging method. The comparison shows excellent agreements in the major features from the stratosphere to the ionosphere including the growth and decay of the major stratospheric sudden warming (SSW) event in 2009. During the major SSW period, a pronounced semidiurnal variation in the F-region electron density and its local-time phase shift similar to the previous observations are reproduced by the model and COSMIC observation. The model suggests that the TEC variation is caused by an enhanced semidiurnal variation in the EXB drift, which is probably related to an amplified semidiurnal migrating tide (SW2) in the lower thermosphere. The model and TIMED/SABER observation show that the SW2 tide amplifies at low latitudes from the stratosphere to the thermosphere as well as the phase variation. Possible mechanisms will be discussed in the presentation.

Research paper thumbnail of Planetary Waves and Midlatitude Sporadic E Layers. Evidence For A Close Relationship

Egs General Assembly Conference Abstracts, 2002

A large-amplitude, 7-day period westward propagating S = 1 planetary wave has been reported from ... more A large-amplitude, 7-day period westward propagating S = 1 planetary wave has been reported from ground radar and satellite wind measurements in the mesosphere lower thermosphere (MLT) during the second half of August and well into September 1993. Following recent suggestions that planetary waves might play a role in the formation of midlatitude sporadic E layers (Es), we have obtained

Research paper thumbnail of A Single-Station Spectral Model of the Monthly Median fo F2 and M(3000)F2

Research paper thumbnail of A single-station spectral model of the monthly median F-region critical frequency

Annals of Geophysics, 1996

Research paper thumbnail of Planetary waves and variability of the semidiurnal tide in the mesosphere and lower thermosphere over Esrange (68°N, 21°E) during winter

Journal of Geophysical Research Space Physics, 2004

The main features of the planetary waves and the variability of the semidiurnal tide with planeta... more The main features of the planetary waves and the variability of the semidiurnal tide with planetary wave periods observed by meteor radar over Esrange (68°N, 21°E) have been investigated. The interval of 39 months covering continuous measurements from October 1999 to December 2002 has been examined. The planetary waves most frequently observed by meteor radar measurements in the mesosphere and lower thermosphere (80-100 km) over Esrange are: 5-, 8-to 10-, 16-, and 23-day waves (the quasi-2-day wave is excluded in this study). They are strongly amplified in the winter. Some differences between high-and middle-latitude planetary waves notwithstanding, the 5-, 10-, and 16-day waves are most probably related to the well-known normal mode. There are some reasons to believe that the vertically upward propagating 23-day wave could be generated by solar forcing. The variability of the semidiurnal tide with periods of planetary waves has been thoroughly studied as well. It is found that in the winter when the planetary waves are significantly amplified, a very strong periodic variability of the semidiurnal tide is observed as well. This result indicates that the most probable mechanism responsible for the periodic tidal variability during winter is in situ nonlinear coupling between tides and planetary waves. Two winter periods have been examined (1999/2000 and 2001/2002) in order to find strong evidence supporting this suggestion. The validity of the frequency, phase, and vertical wavenumber (wavelength) relationship between the prime (the planetary wave and semidiurnal tide) and secondary waves has been established. The novel aspect of this work is that we show for the first time that the calculated vertical structures (vertical wavelengths) of the sum and difference secondary waves, which have very close periods, are actually very different.

Research paper thumbnail of Terdiurnal tidelike variability in sporadic E layers

Journal of Geophysical Research Space Physics, 2006

Time series analysis was performed on a large database of ionosonde recordings taken over 12 year... more Time series analysis was performed on a large database of ionosonde recordings taken over 12 years, for the 6-month period from the beginning of May to the end of October when sporadic E layer occurrence is frequent. The results show that in addition to the well known 24-and 12-hour tidal variations, there is also a weaker but regular 8-hour periodicity in midlatitude sporadic E layers (E s). Statistically, this terdiurnal periodicity is significant and occurs in both the sporadic E layer critical frequency (foEs) and the layer virtual height (h 0 Es), becoming strongest around summer solstice and later in October after a minimum in September. At times a weak 6-hour periodicity can also be present in E s but its effects are much less significant than those of the 8-hour oscillation. The 8-hour periodicity in E s is attributed to the terdiurnal tide, presumably acting through its vertical wind shear forcing of the metallic ions in the lower thermosphere. The relation to the terdiurnal tide was inferred from simultaneous ionosonde recordings from three widely spaced stations in the same midlatitude zone, showing the 8-hour oscillation to be present simultaneously in all ionosonde stations and have phases which are consistent with a westward propagating terdiurnal wave of zonal wave number 3. The present study establishes the regular occurrence of a terdiurnal tidelike oscillation in E s which needs to be incorporated into the physics and modeling of sporadic E layer formation and dynamics.

Research paper thumbnail of Vertical coupling in the atmosphere/ionosphere system - Preface

Journal of Atmospheric and Solar-Terrestrial Physics

Research paper thumbnail of Model of the electron density height profile in the lowest D-region (50 to 75 km)

Advances in Space Research, 1995

Research paper thumbnail of Planetary wave coupling of the atmosphere–ionosphere system during the Northern winter of 2008/2009

Advances in Space Research, 2012

ABSTRACT This paper presents the global spatial (latitude and altitude) structure and temporal va... more ABSTRACT This paper presents the global spatial (latitude and altitude) structure and temporal variability of the ∼23-day ionospheric zonally symmetric (s = 0) planetary wave (PW) seen in the Northern winter of 2008/2009 (October 2008–March 2009). It is shown that these ∼23-day ionospheric oscillations are forced from PWs propagating from below. The COSMIC ionospheric parameters foF2 and hmF2 and electron density at fixed altitudes and the SABER temperatures were utilized in order to define the waves which are present simultaneously in the atmosphere and ionosphere. The long-period PWs from the two data sets have been extracted through the same data analysis method. The similarity between the lower thermospheric ∼23-day (s = 0) temperature PW and its ionospheric electron density response provides valuable and strong experimental evidence for confirming the paradigm of atmosphere–ionosphere coupling.

Research paper thumbnail of Global-scale tidal variability during the PSMOS campaign of June–August 1999: interaction with planetary waves

Journal of atmospheric and solar-terrestrial physics, Nov 30, 2002

During the PSMOS Global-scale tidal variability experiment campaign of June 1–August 31, 1999, a ... more During the PSMOS Global-scale tidal variability experiment campaign of June 1–August 31, 1999, a network of radars made measurements of winds, waves and tides in the mesosphere/lower-thermosphere region over a wide range of latitudes. Clear evidence was found that fluctuations in tidal amplitudes occur on a global scale in both hemispheres, and that at least some of these fluctuations are periodic in nature. Modulation of the amplitude of the 12 h tide was particularly evident at periods of 10 and 16 days, suggesting a non- ...

Research paper thumbnail of Global-scale tidal structure in the mesosphere and lower thermosphere during the PSMOS campaign of June–August 1999 and comparisons with the global-scale wave model

Journal of atmospheric and solar-terrestrial physics, May 7, 2002

Observations of mean winds and semidiurnal and diurnal tides in the mesosphere/lower-thermosphere... more Observations of mean winds and semidiurnal and diurnal tides in the mesosphere/lower-thermosphere (MLT) region were made during the 3-month Planetary-Scale Mesopause Observing System Summer 1999 campaign. Data from 22 ground-based radars (and from two other instruments with measurements for the same period but in 1998) allow us to investigate the ability of the GSWM-00 to simulate the solar tides in the mesopause region (90–95 km). Here we have found that the GSWM-00 provides an increasingly reasonable ...

Research paper thumbnail of Long-term prediction of the foF2 on the rising and falling parts of the solar cycle

Advances in Space Research, 1994

In this paper we intend to enlarge the fof2 long-term prediction accuracy taking into account the... more In this paper we intend to enlarge the fof2 long-term prediction accuracy taking into account the systematic variations of the hysteresis and secular-time phenomena.

Research paper thumbnail of Mesosphere/lower thermosphere prevailing wind model

Advances in Space Research, 2004

... r Physics and Maths Physics, University of Adelaide, Adelaide 5005, Australia. s INPE Aeronom... more ... r Physics and Maths Physics, University of Adelaide, Adelaide 5005, Australia. s INPE Aeronomy Division, CP 515, Sao Jose dos Campos, SP 12200, Brazil. t Department of Physics and Electronics, Rhodes University, PO Box 94, Grahamstown 6140, Republic of SouthAfrica. ...

Research paper thumbnail of Quasi-periodic fluctuations in ionospheric absorption in relation to planetary activity in the stratosphere

Journal of atmospheric and …, 1991

Quasi-periodic fluctuations (2-15 days) in ionospheric absorption along three radio paths in Cent... more Quasi-periodic fluctuations (2-15 days) in ionospheric absorption along three radio paths in Central and Southern Europe are investigated for three winter periods 1985/86, 1986/87 and 1987/88. The periods of dominant fluctuations in absorption and the time variations of their amplitudes are similar for all radio paths and every winter period. The shorter-period fluctuations are found to be associated with enhancements of planetary wave two activity in the stratosphere (30 hPa, 60"N), while longer period fluctuations appear to be associated with intensification of planetary wave one activity in the stratosphere.

Research paper thumbnail of Planetary waves and midlatitude sporadic E layers: Strong experimental evidence for a close relationship

J. Geophys. Res, 2002

Dora Pancheva Department of Physics, University of Wales, Aberystwyth, Wales, UK Received 17 July... more Dora Pancheva Department of Physics, University of Wales, Aberystwyth, Wales, UK Received 17 July 2001; revised 24 September 2001; accepted 28 September 2001; published 19 June 2002. [1] A large-amplitude, 7-day period westward propagating S = 1 planetary wave ...

Research paper thumbnail of Planetary wave activity in the lower ionosphere during CRISTA I campaign in autumn 1994 (October-November)

Annales Geophysicae, 1998

On the basis of MEM spectrum analysis, the main planetary scale¯uctuations formed in the lower io... more On the basis of MEM spectrum analysis, the main planetary scale¯uctuations formed in the lower ionosphere are studied over a period of 3±25 days during the CRISTA campaign (October-November 1994). Three dominant period bands are found: 3±5, 6±8 and 15±23 (mainly 16±18) days. For 7±8 and 16±18 daȳ uctuations, propagation was eastward with wave numbers K = 3 and K = 1, respectively. The magnitude of planetary wave activity in the mid-latitudes of the Northern Hemisphere during the CRISTA campaign seems to be fairly consistent with the expected undisturbed normal/climatological state of the atmosphere at altitudes of 80±100 km.

Research paper thumbnail of Non-linear interaction of tides and planetary waves in the mesosphere and lower thermosphere: observations over Europe

Physics and Chemistry of the Earth, Part C: Solar, Terrestrial & Planetary Science

ABSTRACT

Research paper thumbnail of Global Empirical Model of the TEC Response to Geomagnetic Activity and Forcing from Below

Research paper thumbnail of Influence of Solar Activity on the Summer Electron Density Profiles in Thelower Midlatitude D-Region

Dokladi Na B Lgarskata Akademiâ Na Naukite, 1998

Research paper thumbnail of Quasiperiodic oscillations in the ionospheric absorption of solar and inner-atmospheric origin

A band-pass filter is used to study two aspects of a wave response in the lower ionosphere with a... more A band-pass filter is used to study two aspects of a wave response in the lower ionosphere with a period close to that of the solar rotation period. This response was brought about by both short-period (about 27 d) oscillations of solar activity and waves generated inside the atmosphere itself. In the first instance, the fluctuations generated in the D-region ionosphere (80-95 km) are synchronous with the 27-day oscillations, and in the lower D-region (from the base of the ionosphere to about 75 km) there is no noticeable reaction. A strong wave reaction is observed in the wintertime upper and lower D-region of the ionosphere when the 27-day oscillations are close to nonexistent. The wave reaction has a period of 24-28 days and consists of waves generated inside the atmosphere itself and propagating vertically upward. On average, the fluctuation amplitude in the field of the ionospheric absorption increases with height. The average period also changes with height; for the lower D-region it consists of 24-25 days, while for the upper region it is 26-27 days.

Research paper thumbnail of Tidal variability during stratospheric sudden warming in 2009: Comparison between GAIA model and COSMIC and TIMED/SABER observations

ABSTRACT We compare results from a whole atmosphere-ionosphere coupled model, GAIA, and from the ... more ABSTRACT We compare results from a whole atmosphere-ionosphere coupled model, GAIA, and from the COSMIC and TIMED/SABER observations during 2008/2009 northern winter season. The GAIA model has assimilated meteorological reanalysis data by a nudging method. The comparison shows excellent agreements in the major features from the stratosphere to the ionosphere including the growth and decay of the major stratospheric sudden warming (SSW) event in 2009. During the major SSW period, a pronounced semidiurnal variation in the F-region electron density and its local-time phase shift similar to the previous observations are reproduced by the model and COSMIC observation. The model suggests that the TEC variation is caused by an enhanced semidiurnal variation in the EXB drift, which is probably related to an amplified semidiurnal migrating tide (SW2) in the lower thermosphere. The model and TIMED/SABER observation show that the SW2 tide amplifies at low latitudes from the stratosphere to the thermosphere as well as the phase variation. Possible mechanisms will be discussed in the presentation.

Research paper thumbnail of Planetary Waves and Midlatitude Sporadic E Layers. Evidence For A Close Relationship

Egs General Assembly Conference Abstracts, 2002

A large-amplitude, 7-day period westward propagating S = 1 planetary wave has been reported from ... more A large-amplitude, 7-day period westward propagating S = 1 planetary wave has been reported from ground radar and satellite wind measurements in the mesosphere lower thermosphere (MLT) during the second half of August and well into September 1993. Following recent suggestions that planetary waves might play a role in the formation of midlatitude sporadic E layers (Es), we have obtained

Research paper thumbnail of A Single-Station Spectral Model of the Monthly Median fo F2 and M(3000)F2

Research paper thumbnail of A single-station spectral model of the monthly median F-region critical frequency

Annals of Geophysics, 1996

Research paper thumbnail of Planetary waves and variability of the semidiurnal tide in the mesosphere and lower thermosphere over Esrange (68°N, 21°E) during winter

Journal of Geophysical Research Space Physics, 2004

The main features of the planetary waves and the variability of the semidiurnal tide with planeta... more The main features of the planetary waves and the variability of the semidiurnal tide with planetary wave periods observed by meteor radar over Esrange (68°N, 21°E) have been investigated. The interval of 39 months covering continuous measurements from October 1999 to December 2002 has been examined. The planetary waves most frequently observed by meteor radar measurements in the mesosphere and lower thermosphere (80-100 km) over Esrange are: 5-, 8-to 10-, 16-, and 23-day waves (the quasi-2-day wave is excluded in this study). They are strongly amplified in the winter. Some differences between high-and middle-latitude planetary waves notwithstanding, the 5-, 10-, and 16-day waves are most probably related to the well-known normal mode. There are some reasons to believe that the vertically upward propagating 23-day wave could be generated by solar forcing. The variability of the semidiurnal tide with periods of planetary waves has been thoroughly studied as well. It is found that in the winter when the planetary waves are significantly amplified, a very strong periodic variability of the semidiurnal tide is observed as well. This result indicates that the most probable mechanism responsible for the periodic tidal variability during winter is in situ nonlinear coupling between tides and planetary waves. Two winter periods have been examined (1999/2000 and 2001/2002) in order to find strong evidence supporting this suggestion. The validity of the frequency, phase, and vertical wavenumber (wavelength) relationship between the prime (the planetary wave and semidiurnal tide) and secondary waves has been established. The novel aspect of this work is that we show for the first time that the calculated vertical structures (vertical wavelengths) of the sum and difference secondary waves, which have very close periods, are actually very different.

Research paper thumbnail of Terdiurnal tidelike variability in sporadic E layers

Journal of Geophysical Research Space Physics, 2006

Time series analysis was performed on a large database of ionosonde recordings taken over 12 year... more Time series analysis was performed on a large database of ionosonde recordings taken over 12 years, for the 6-month period from the beginning of May to the end of October when sporadic E layer occurrence is frequent. The results show that in addition to the well known 24-and 12-hour tidal variations, there is also a weaker but regular 8-hour periodicity in midlatitude sporadic E layers (E s). Statistically, this terdiurnal periodicity is significant and occurs in both the sporadic E layer critical frequency (foEs) and the layer virtual height (h 0 Es), becoming strongest around summer solstice and later in October after a minimum in September. At times a weak 6-hour periodicity can also be present in E s but its effects are much less significant than those of the 8-hour oscillation. The 8-hour periodicity in E s is attributed to the terdiurnal tide, presumably acting through its vertical wind shear forcing of the metallic ions in the lower thermosphere. The relation to the terdiurnal tide was inferred from simultaneous ionosonde recordings from three widely spaced stations in the same midlatitude zone, showing the 8-hour oscillation to be present simultaneously in all ionosonde stations and have phases which are consistent with a westward propagating terdiurnal wave of zonal wave number 3. The present study establishes the regular occurrence of a terdiurnal tidelike oscillation in E s which needs to be incorporated into the physics and modeling of sporadic E layer formation and dynamics.