Gravity Waves

In this work, I have considered slow roll inflation in theories of two scalar fields in the context of Starobinsky gravity. It is found that the inflationary observables, the spectral indices and tensor to scalar ratio at Hubble exit, depends on theory parameters, (Mp, M) and scalar potential parameters, in complicated manner due to the presence of two scalar fields in an unusual background dynamical nature of spacetime.

В работе вводится и разворачивается Теория Искривлённого Пространства (ТИП) — онтология, где пространство имеет четыре равноправные координаты, время t является абсолютным параметром эволюции, а физика наблюдаемого мира возникает как проекция 4D‑динамики на 3D‑срез. Ключевой аксиомой ТИП служит сохранение 4D‑объёма (глобальная SL(4,ℝ)‑симметрия). Из неё по теореме Нётер следуют четыре фундаментальных сохраняющихся тока: заряда, энергии, осевой (момент) и гомотетический (масштаб). Центральный результат — закон плато: в устойчивых геометриях (диск, сфера) соответствующие интегралы потока становятся константами, задавая асимптотическую кинематику от атома до галактики без привлечения тёмной материи.

Закон плато формулируется в операциональном виде на 3D‑срезе с мерой J3=det Q3 и анизотропией согласования Aij:
- Сфера (радиальный перенос, изотропия): Ks=R^2 J3 ρ(R) u∗(R)=const, что при медленном изменении J3 восстанавливает ньютоновский спад v(R)∝R^−1/2 во внешних областях.
- Тонкий диск (перенос в плоскости): Ka=R J3 ARR Σ(R) uR(R)=const, и при квазипостоянных J3 ARR и u∗ даёт плоскую кривую вращения v(R)=const (закон Местела) — без тёмной материи.
- В разреженных гало из инварианта R^2ρ=const следует M(R)∝R и выход ускорения к порогу a0≈10^−10 м/с^2, связанного в ТИП с глобальным вращением вокруг четвёртой оси.

На уровне частиц и полей ТИП даёт единую кинематическую оболочку: скалярные потенциалы входят мультипликативно в «маску» энергии покоя 𝓜(x,t)=√∏i(1−2Φi/c^2), а все калибровочные взаимодействия — через минимальное сцепление в импульсе. Квантование универсальной связи энергии–импульса приводит к обобщённым уравнениям Клейна–Гордона и Дирака; нерелятивистский предел даёт уравнение Паули. В электромагнетизме магнитное поле имеет проекционную (кинематическую) природу B=(1/c^2) v×E; в неабелевых полях (слабое/сильное) «магнитные» компоненты являются динамическими и не редуцируются к проекции из‑за самодействия.

Гравитационный сектор формализован через эффективное 3D‑действие, воспроизводящее ньютоновскую нормировку ΔΦ=4πGρ в слабом поле и позволяющее решать прикладные задачи: вращательные кривые, линзирование, чёрные дыры (тень, фотосфера, ISCO, задержка Шапиро). Показано, что классические наблюдаемые величины совпадают со стандартными результатами, при этом ТИП предсказывает фазовые эффекты (моно-дромии, эхо‑сигналы при кольцевании), доступные для проверки гравитационно‑волновыми и поляриметрическими измерениями.

Методика проверена на реальных данных без подгонок «по месту»: кривые вращения и фотометрия каталога SPARC (например, NGC 3198, NGC 2403, UGC 2885), карликовые сфероидалы Draco и Sculptor, ультрадиффузная NGC 1052‑DF2 (согласованный инвариант в сферической зоне), а также системы линзирования различного масштаба (SDSS J2141, ESO 325‑G004, Abell 1689) — расчёт углов отклонения выполняется из Φтип(r) при фиксированных входах (MGE, M/L, fgas, угловые расстояния), согласуясь с наблюдениями в пределах статистических ошибок. Космологический раздел формулирует фоновые уравнения и диагностирует совместимость с положением первого акустического пика СМВ без введения тёмной материи как компоненты.

Работа демонстрирует три свойства самодостаточной альтернативы: (1) внутренняя непротиворечивость аксиоматики и выводов; (2) количественное согласие с данными на множестве масштабов при фиксированных нормировках; (3) новые фальсифицируемые предсказания (пороговое ускорение, фазовая структура гравитационных сигналов, инварианты потоков), которые отличают ТИП от стандартных моделей.

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## Ключевая формулировка закона плато (для карточки записи)

- Сферический режим: dR(R^2 J3 ρ u∗)=0 ⇒ R^2 J3 ρ u∗=const; следствие: M(R)∝R, v(R)∝R^−1/2, a(R)→a0 на хвосте гало.
- Дисковый режим: dR(R J3 ARR Σ uR)=0 ⇒ R J3 ARR Σ uR=const; следствие: v(R)=const при квазипостоянных ARR, J3 и переносе в плоскости.
- Операционная мера и анизотропия: J3=det Q3>0, Aij — безразмерный тензор «быстрых» направлений согласования det Q=1; u∗ — скорость фронта согласования, |u∗|<c.

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## Новизна

- Универсальная операциональная формулировка законов сохранения через нётеровские токи ТИП с явной мерой J3 и анизотропией Aij.
- Дедуктивный вывод закона плато для дисковой и сферической геометрий без тёмной материи.
- Единая формула энергии–импульса с маской, охватывающая все четыре взаимодействия, и её квантование (КГФ/Дирак/Паули).
- Проекционная интерпретация магнитного поля (абелева) и разграничение с неабелевыми полями.
- Предсказуемые фазовые эффекты в сильнополевых режимах (чёрные дыры) при согласии классических наблюдаемых.

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## Валидирующие расчёты и данные

- Галактики SPARC: проверка инвариантов Ka, Ks; плоские кривые вращения без тёмной материи; оценка a0≈10^−10 м/с^2.
- Карликовые сфероидалы Draco, Sculptor: плоскость R^2ρ u∗=const в сферической зоне; сравнение с MOND/ΛCDM.
- NGC 1052‑DF2: реконструкция сферического инварианта из динамической массы.
- Линзирование: SDSS J2141, ESO 325‑G004, Abell 1689 — согласие углов отклонения при фиксированных входах (MGE, M/L, fgas, D_A).

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## Ключевые слова

Теорема Нётер; закон плато; Теория Искривлённого Пространства; SL(4,ℝ); инварианты потоков; плоские кривые вращения; критическое ускорение a0; гравитационное линзирование; обобщённые уравнения Клейна–Гордона и Дирака; маска скалярных потенциалов; проекционная природа магнитного поля; SU(3)×SU(2)×U(1); чёрные дыры; эхосигналы; СМВ.

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## Рекомендуемое краткое описание (для превью)

Мы формулируем закон плато — универсальное следствие нётеровских симметрий в ТИП: в дисках R J3 ARR Σ uR=const, в сферах R^2 J3 ρ u∗=const. Из него следуют плоские кривые вращения и пороговое ускорение a0≈10^−10 м/с^2 без тёмной материи. Теория даёт единую формулу энергии–импульса (маска скалярных потенциалов + минимальное сцепление), обобщённые КГФ/Дирак, и согласуется с данными (SPARC, Draco/Sculptor, DF2, линзирование), предлагая новые фальсифицируемые предс

The uploaded document presents a comprehensive and highly theoretical model for the deterministic evolution of the Solar System, spanning 13 billion years from its formation to the Sun's eventual transformation into a white dwarf. This model is based on the author's "Unified Theory of the Cyclic Quantum Elastic Universe" (ЕТЦКВ).

**Core Theory: Unified Theory of the Cyclic Quantum Elastic Universe (ЕТЦКВ)**

The foundation of this model is the ЕТЦКВ, which proposes that spacetime is not empty but a dynamic physical substance called a "Quantum Elastic Network" (QEN). This network possesses physical properties like:
*  **Time Energy Density (ρt):** A key variable where gradients generate forces.
*  **Elastic Modulus (E):** Related to the "stiffness" of spacetime, calibrated to Planck pressure.
*  **Poisson's Ratio (σ):** Describes transverse deformation, evolving over time.
*  **Decoherence Rate (Γ D):** Characterizes the loss of quantum coherence, changing with the Sun's evolution.

The theory modifies Einstein's field equations to include terms for the dynamics and self-interaction of this time energy density. Crucially, it posits that **all fundamental interactions, including non-gravitational effects (like the Yarkovsky effect and Poynting-Robertson drag), are manifestations of the interaction with the gradient of ρt.**

**Key Predictions and Findings of the Solar System Evolution Model**

1.  **Evolution of the Sun:** The model details the Sun's phases (Main Sequence, Subgiant, Red Giant, Planetary Nebula, White Dwarf) and how each phase alters the QEN parameters (E, σ, Γ D), which in turn affect planetary dynamics.
2.  **Fate of the Inner Planets:**
    *  **Mercury & Venus:** Predicted to be engulfed by the Sun around 5.0-5.2 billion years from now during its Red Giant phase. QEN elasticity is said to delay this by ~0.2 billion years compared to classical models.
    *  **Earth & Moon:** The system is predicted to reach "mutual synchronization" (Earth's day = Moon's orbital period) in ~3.2 billion years, with a final Earth-Moon distance of 546,283 km. The probability of Earth being engulfed by the Sun at 5.5 billion years is estimated at 65%, reduced by 7% due to QEN effects.
3.  **Mars and its Moons:**
    *  **Phobos:** Predicted to reach its Roche limit and be destroyed by Mars in ~4.5 billion years. QEN elasticity is said to slow its inward spiral by 15%.
    *  **Deimos:** Expected to remain stable, with Phobos's debris forming rings around Mars.
4.  **Outer Planets (Jupiter, Saturn, Uranus, Neptune, Pluto):** The model predicts these planets will maintain stable orbits due to the stabilizing effect of QEN elasticity, which reduces their sensitivity to external perturbations by factors of 4-52. Pluto's probability of being ejected is reduced from 5.2% (classical) to 0.1%.
5.  **Asteroids and Comets:**
    *  The Asteroid Belt and Kuiper Belt are predicted to expand outward as the Sun loses mass.
    *  The probability of asteroid Apophis colliding with Earth in 4.5 billion years is estimated at 2.5%, but QEN effects are said to reduce this by 30-40%.
    *  Comet Halley has an 85% probability of its nucleus evaporating during the Sun's Red Giant phase, reduced to 70% by QEN.
6.  **External Influences:**
    *  The model incorporates the effects of stellar flybys (e.g., Proxima Centauri in 1.3 million years, Scholz's Star in 4.5 billion years) and galactic tidal forces.
    *  QEN elasticity is claimed to suppress the disruptive effects of these events by 55-75%.

**Model Validation and Comparison**

*  **Validation:** The author claims the model's parameters were calibrated using historical data (e.g., lunar distance, Earth's rotation period 4.5 billion years ago) and shows good agreement with independent paleomagnetic, isotopic, and cratering data, with an average discrepancy of 3.5%, claimed to be significantly better than classical models (15-25%).
*  **Determinism vs. Chaos:** A central philosophical claim is that the N-body problem's apparent chaos is not ontological but epistemological, arising from ignoring the physical nature of spacetime. The model reportedly yields a negative Lyapunov exponent (λ = -1.8×10⁻¹⁵ s⁻¹), indicating asymptotic stability and determinism.
*  **Comparison with Alternatives:** The ЕТЦКВ is presented as superior to classical mechanics (longer predictive horizon, lower error) and the multiverse hypothesis (more economical, testable predictions) by explaining the "fine-tuning" of constants through their evolution.

In conclusion, the document presents an ambitious, all-encompassing theoretical framework that seeks to deterministically model the entire lifecycle of the Solar System by redefining the nature of spacetime itself as an elastic quantum medium. It makes specific, long-term predictions about the fate of planets and smaller bodies, attributing stabilizing effects to the proposed elastic properties of this medium.

In this appendix we discuss some Monte Carlo simulations to evaluate the accuracy of our three-stage estimator in finite samples. We then provide some descriptives and details on the computation of the stream of earnings in the application, as well as additional results and robustness checks. Finally, the third section is devoted to the proofs of our results.

Atmospheric dynamics comprise of a multitude of phenomena from various sources that affect the entire climate of the globe. Some of these phenomena include Atmospheric Gravity Waves which are ubiquitous features around the planet. They are important mechanisms for the transport of momentum and energy from the lower atmosphere to the upper atmosphere. The sun is the ultimate source of energy for the earth and the primary driver of atmospheric dynamics. The 11-year solar cycle of the sun has had a noticeable effect on the overall climate of the earth in the past. More recent work has seen the diurnal tides being directly influenced by the change in solar energy over the solar cycle at the South Pole. The different types of atmospheric waves interact with each other in complex manners that are still a subject of research today. Gravity waves are known to be modulated by solar tides and vice versa so a change in the tides will induce a change in gravity waves. The solar cycle influence on tides can then be seen overall in gravity wave wavelengths and speeds. A CCD Spectrometer is used to gather temperatures and brightness's of two separate airglow layers in the upper atmosphere at 87km (OH) and 93km (O 2 ). Two different years are chosen to be analyzed for solar cycle dependencies. One year is 2002, during the previous time of maximum solar activity and the other is 2010, just after the last minimum of solar activity. Time series of temperatures and brightness's are analyzed for gravity Without this opportunity I would not be where I am today. Thanks go to my Mother, Carole Rogers and my Father, Samuel Agner Jr. for your unconditional love and support throughout my entire life and for instilling in me your values, morals and ethics that guide me. Thanks also go to my older sister, Amanda and my younger sister, Sarah. We have all been through good times and bad times and have emerged from them with stronger bonds than before. To my mother-in-law and sister-in-law I would like to express my gratitude for everything you have given both of us, from coming all the way from India for our wedding and for your love from half-way across the world. Thanks are given to my entire family for everything you have given me throughout my life.

Atmospheric dynamics comprise of a multitude of phenomena from various sources that affect the entire climate of the globe. Some of these phenomena include Atmospheric Gravity Waves which are ubiquitous features around the planet. They are important mechanisms for the transport of momentum and energy from the lower atmosphere to the upper atmosphere. The sun is the ultimate source of energy for the earth and the primary driver of atmospheric dynamics. The 11-year solar cycle of the sun has had a noticeable effect on the overall climate of the earth in the past. More recent work has seen the diurnal tides being directly influenced by the change in solar energy over the solar cycle at the South Pole. The different types of atmospheric waves interact with each other in complex manners that are still a subject of research today. Gravity waves are known to be modulated by solar tides and vice versa so a change in the tides will induce a change in gravity waves. The solar cycle influence on tides can then be seen overall in gravity wave wavelengths and speeds. A CCD Spectrometer is used to gather temperatures and brightness's of two separate airglow layers in the upper atmosphere at 87km (OH) and 93km (O 2 ). Two different years are chosen to be analyzed for solar cycle dependencies. One year is 2002, during the previous time of maximum solar activity and the other is 2010, just after the last minimum of solar activity. Time series of temperatures and brightness's are analyzed for gravity Without this opportunity I would not be where I am today. Thanks go to my Mother, Carole Rogers and my Father, Samuel Agner Jr. for your unconditional love and support throughout my entire life and for instilling in me your values, morals and ethics that guide me. Thanks also go to my older sister, Amanda and my younger sister, Sarah. We have all been through good times and bad times and have emerged from them with stronger bonds than before. To my mother-in-law and sister-in-law I would like to express my gratitude for everything you have given both of us, from coming all the way from India for our wedding and for your love from half-way across the world. Thanks are given to my entire family for everything you have given me throughout my life.

Gravity waves and thermal tides are two of the most important dynamical features of the atmosphere. They are both generated in the lower atmosphere and propagate upward transporting energy and momentum to the upper atmosphere. This dissertation focuses on the interaction of these waves in the Mesosphere and Lower Thermosphere (MLT) region of the atmosphere using both observational data and Global Circulation Model (GCMs). The first part of this work focuses on observations of gravity wave interactions with the tides using both LIDAR data at the Star Fire Optical Range (SOR, 35◦N, 106.5◦W) and a meteor radar data at the Andes LIDAR Observatory (ALO, 30.3◦S, 70.7◦W). At SOR, the gravity waves are shown to enhance or damp the amplitude of the diurnal variations dependent on altitude while the phase is always delayed. The results compare well with previous mechanistic model results and with the Japanese Atmospheric General circulation model for Upper Atmosphere Research (JAGUAR) high re...

Wave phenomena are ubiquitous across physics, appearing in mechanical, acoustic, electromagnetic, quantum, and gravitational systems. Traditionally, each wave type has its own governing equation, leading to fragmented descriptions. In this paper, we introduce a Universal Wave Equation (UWE) capable of describing all linear and nonlinear wave phenomena. By adjusting system-specific parameters and interpreting Ψ according to the physical context, the UWE can reproduce classical wave equations such as the acoustic wave equation, the electromagnetic wave equation, the Schrödinger equation, the Klein-Gordon equation, and the Einstein field equations for gravitational waves. This framework provides a unified mathematical foundation for wave physics and opens pathways for cross-disciplinary analyses and simulations.

This article analyzes (one-dimensional) nonlinear wave propagation over a disordered fluid body having a small viscosity. The lower boundary is disordered and modeled by a random process. As a pulse shaped nonlinear wave propagates over this turbulent boundary, the velocity and wave elevation are viewed as random fields. Starting from first principles the eddy viscosity is characterized and shown to depend on different scales. This is captured as the leading order pseudodifferential operator resulting from the asymptotic analysis of stochastic differential equations. A discussion is provided showing that mean-field theory would have not captured the correct attenuation rate for the large scale object. Numerical results are provided illustrating the accuracy of the eddy viscosity expression.

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries ͑KdV͒ equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case.

In this paper we have tried to deduce the possible origin of particle and evolution of their intrinsic properties through spiral dynamics. We consider some of the observations which include exponential mass function of particles following a sequence when fitted on logarithmic potential spiral, inwardly rotating spiral dynamics in Reaction-Diffusion System, the separation of Electron's Spin-Charge-Orbit into quasi-particles. The paper brings a picture of particles and their Anti Particles in spiral form and explains how the difference in structure varies their properties. It also explains the effects on particles in Accelerator deduced through spiral dynamics.

This paper concerns the ubiquitous bias problemin data assimilation, which is caused by the presence of systematic (as opposed to random) errors in both models and observations. Systematic model errors can arise, for example, from inaccurate land-surface forcing, poor resolution of the boundary layer, simplified representations of moist physics and clouds, and various other model imperfections. Observation biases for different types of instruments are often caused by specific aspects of the measurement process, or—in the context of data assimilation—by approximations in the observation operators that are used to represent the relationship between the observables and the model variables. It takes a great deal of work to screen the observations and correct them for known biases in order to extract the information that is actually useful to assimilate (e.g. McNally et al. 2000). However, we will assume in what follows that all this has been done, and that any remaining bias in the obse...

The Mars Global Surveyor (MGS) z -axis accelerometer has obtained over 200 vertical structures of thermospheric density, temperature, and pressure, ranging from 110 to 170 kilometers, compared to only three previous such vertical structures. In November 1997, a regional dust storm in the Southern Hemisphere triggered an unexpectedly large thermospheric response at mid-northern latitudes, increasing the altitude of thermospheric pressure surfaces there by as much as 8 kilometers and indicating a strong global thermospheric response to a regional dust storm. Throughout the MGS mission, thermospheric density bulges have been detected on opposite sides of the planet near 90°E and 90°W, in the vicinity of maximum terrain heights. This wave 2 pattern may be caused by topographically-forced planetary waves propagating up from the lower atmosphere.

The transfer of momentum due to non-orographic Gravity Waves (GWs) significantly regulates the Martian middle-upper atmospheric dynamics. Thus, these waves influence the transport of tracers and escape in the thermosphere. However, models assume that the non-orographic GWs are emitted from a constant source level that approximates the averaged Planetary Boundary Layer (PBL). We move on to impose that the emission of the waves follows the top of a real-time evaluated PBL to account for the diurnal cycle of the waves' source altitudes and implement this improvement in the Mars Planetary Climate Model (Mars PCM). In the absence of the PBL during the night, the non-orographic GWs are assumed to be launched at altitudes near the surface following Hinson and Wilson (2023, https://doi.org/10.1016/j.icarus.2022.115420)'s results. Sensitivity tests with the Mars PCM show that non-orographic GWs are built up efficiently during the (polar) night. With the new scheme, the angular momentum in the upper atmosphere is enhanced. Additionally, simulations recover the "cold pockets" in temperature observed by the Mars Climate Sounder at 80-100 km and capture "deep drops" of the atmospheric species recorded by the Neutral Gas and Ion Mass Spectrometer in the polar night. Plain Language Summary Martian gravity waves are variations in the air caused by the up-anddown movement of the lower atmosphere, which is mostly driven by the heating from the Sun. At night, these waves are not forced anymore. However, new research shows that these waves can still form near the surface at night due to wind interactions with topography. Previous models treated these waves as coming from an average height in the atmosphere, but this doesn't fully capture their behavior, especially since this height changes throughout the day. In this study, we improved the modeling by launching these waves from the exact height where the waves are expected to be emitted. This new approach helps explain mysterious cold spots in Mars' upper atmosphere and sudden drops in air density during the (polar) night, which have been observed by various missions. Understanding these processes better can help us predict Mars' weather and climate, which is important for future missions to the planet.

In this paper, the non-orographic gravity waves (GW) parameterization of the Mars Planetary Climate Model (PCM) previously implemented by Gilli et al. (2020, https://doi.org/10.1029/2018JE005873) is revisited and extended to the exobase (∼250 km). The simulations performed with the new scheme correct some known biases in the modeled thermal tide amplitudes and polar warming, improving the agreement with Mars Climate Sounder (MCS) observed thermal structures and tides below ∼100 km. Additionally, we find that the simulated densities above 150 km are compatible with NGIMS (Neutral Gas and Ion Mass Spectrometer) measured abundances. Large drag depositions ranging up to >∼950 m s−1 sol−1 are induced at altitude of 90–170 km due to the wave saturation (breaking) and depletion, leading to winds damped to magnitudes of ∼150–225 and ∼80 m s−1 in the zonal and meridional directions, respectively. Resulting temperature variations are ∼±10–30 K or 5%–10% at most latitudes except in the polar regions (where they can reach ∼±30–60 K). The results indicate that non-orographic GW play a significant role in the dynamics of the middle-upper atmosphere of Mars via the induced transfer of momentum and energy from the lower atmosphere.

The cell-integrated semi-Lagrangian method, in which trajectories from the corner points of a grid cell define its extent at a previous time, may be applied to a set of equations on Lagrangian form derived from the complete set of primitive equations to construct a numerical model which conserves exactly the discrete forms of the global integrals constraints of mass, momentum, entrophy and total energy. Due to the fulfilment of these integral constraints one should expect the numerical model to be absolutely stable. Experiments with a simple onedimensional shallow water model show, however, that a time step dependent instability develops when a CFL criterion for gravity waves is exceeded. Analysis of experiments with one-dimensional shallow water models unveil the mechanism of the instability. Using again for simplicity one-dimensional models a main achievement is a successful implementation of the semi-implicit time stepping scheme in the cell-integrated models.

Solar occultations performed by the Nadir and Occultation for MArs Discovery (NOMAD) ultraviolet and visible spectrometer (UVIS) onboard the ExoMars Trace Gas Orbiter (TGO) have provided a comprehensive mapping of atmospheric ozone density. The observations here extend over a full Mars year (MY) between April 21, 2018 at the beginning of the TGO science operations during late northern summer on Mars (MY 34, Ls = 163°) and March 9, 2020 (MY 35). UVIS provided transmittance spectra of the Martian atmosphere allowing measurements of the vertical distribution of ozone density using its Hartley absorption band (200–300 nm). The overall comparison to water vapor is found in the companion paper to this work (Patel et al., 2021, https://doi.org/10.1029/2021JE006837). Our findings indicate the presence of (a) a high‐altitude peak of ozone between 40 and 60 km in altitude over the north polar latitudes for at least 45% of the Martian year during midnorthern spring, late northern summer‐early ...

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This study evaluates the suitability of the Spalart-Allmaras (SA) turbulence model for low-Reynolds number internal flows using Computational Fluid Dynamics (CFD). The domain consists of a 5 mm diameter pipe that extends 150 mm before diverging into five symmetric, curved channels of equal diameter and approximate length. These channels reconverge into a single outlet pipe, matching the inlet in geometry. A steady, incompressible flow of air enters at a velocity of 0.001 m/s, while the outlet is maintained at zero gauge pressure. The estimated Reynolds number (Re ≈ 3.38) confirms laminar conditions, yet the SA model is applied to analyze its behavior under such flow regimes. Simulations conducted in ANSYS Fluent reveal negligible turbulence intensity, near-uniform flow distribution, and minimal wall shear stress throughout the domain. The results indicate that the SA model introduces artificial eddy viscosity, leading to potentially nonphysical turbulence effects in laminar conditions. These findings suggest that laminar models are more appropriate for internal flows of this nature and highlight the importance of Reynolds-number-based turbulence model selection.

Using a two-dimensional Fourier decomposition and a four-dimensional ray-tracing technique, the propagating characteristics and source mechanisms of mesoscale gravity waves simulated in idealized baroclinic jet-front systems are investigated. The Fourier decomposition successfully separates the simulated gravity waves from a complex background flow in the troposphere. Four groups of gravity waves in the lower stratosphere are identified from the spectral decomposition. One is a northward-propagating short-scale wave packet with horizontal wavelength of ϳ150 km, and another is a northeastward-propagating mediumscale wave packet with horizontal wavelength of ϳ350 km. Both of these are most pronounced in the exit region of the upper-tropospheric jet. A third group exists in the deep trough region above (and nearly perpendicular to) the jet, and a fourth group far to the south of the jet right above the surface cold front, both of which are short-scale waves and have a horizontal wavelength of ϳ100-150 km. Ray-tracing analysis suggests that the medium-scale gravity waves originate from the upper-tropospheric jet-front system where there is maximum imbalance, though contributions from the surface fronts cannot be completely ruled out. The shorter-scale, northward-propagating gravity waves in the jet-exit region, on the other hand, may originate from both the upper-tropospheric jet-front system and the surface frontal system. The shorter-scale gravity waves in the deep trough region across the jet (and those right above the surface cold fronts) are almost certain to initiate from the surface frontal system. Ray-tracing analysis also reveals a very strong influence of the spatial and temporal variability of the complex background flow on the characteristics of gravity waves as they propagate.

ARISE proposes to design a new infrastructure that integrates different station networks in order to provide a new &quot;3D&quot; image of the atmospheric dynamics from the ground up to the mesosphere with unprecedented spatio-temporal resolution. The implied networks are: - the International infrasound network developed for the verification of the Comprehensive nuclear Test Ban Treaty (CTBT). This system is unique by its quality for infrasound and atmospheric wave observations, - the Network for the Detection of Atmospheric Composition Changes (NDACC) which uses Lidar to measure stratospheric dynamics, - the Network for the Detection of Mesopause Changes (NDMC), dedicated to airglow layer measurements in the mesosphere, and additional complementary stations and satellite data. The infrastructure extends across Europe and outlying regions, including polar and equatorial regions. The measurements will be used to improve the parameterization of gravity waves in the stratosphere to bet...

We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. The coupling is preserved under only one symmetry, but there are a number of invariant subspaces and degenerate bifurcations forced by the coupling structure, and we investigate these. We show that the system can have a robust attractor that responds to a specific detuning ∆ between certain pairs of the oscillators by a breaking of phase locking for arbitrary ∆ > 0 but not for ∆ ≤ 0. As the dynamical mechanism behind this is a particular type of heteroclinic network, we call this a 'heteroclinic ratchet' because of its dynamical resemblance to a mechanical ratchet.

Context. Gravity waves redistribute energy and momentum between the lower and upper atmosphere, thus providing vertical coupling between layers, and they affect the state, dynamics, and variability of the upper atmosphere. The statistics of gravity wave activity on Mars is poorly explored but is required in order to characterize the atmospheric circulation and to constrain numerical models. Aims. We present the gravity wave statistics accumulated over two Martian years: from the second half of Martian year 34 to the middle of Martian year 36 (May 2018 to February 2022). The statistics includes seasonal and latitude distributions of the wave potential energy and drag, serving to represent the wave activity and impact on the atmospheric dynamics. Methods. The observations were performed by the middle-and near-infrared spectrometers of the Atmospheric Chemistry Suite on board the ExoMars Trace Gas Orbiter. The temperature profiles we obtained independently from both channels during simultaneous measurements show a good agreement, thus providing verification and enhancing confidence in the data. The gravity wave parameters included amplitudes of temperature fluctuations, potential energy per unit mass, and wave drag. These parameters were retrieved at altitudes up to 160 and 100 km from the middle-and near-infrared channels, respectively. Results. A comparison of the data obtained during the global dust storm of Martian year 34 with the corresponding period of Martian year 35 without a storm revealed a reduction of wave activity in mid-latitudes, which is in agreement with previous observations, and enhancement in the polar regions of the southern hemisphere, which was not predicted by simulations with a high-resolution circulation model.

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the Universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the Universe. We carry out a search for the stochastic background with the latest data from the LIGO and Virgo detectors. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of Ω_{GW}(f)=Ω_{α}(f/f_{ref})^{α}, we place 95% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5-1726 Hz. In the frequency band of 41.5-169.25 Hz for a spectral index of α=0, we constrain the energy density of the stochastic background to be…

In this paper we present and discuss observational results on low-latitude mesospheric turbulence obtained from a coordinated experiment made using a Langmuir probe (LP) onboard a rocket launched from Sriharikota (13.6 N, 80.2 E) and the mesosphere-stratosphere-troposphere (MST) radar from Gadanki (13.5 N, 79.2 E) on 8 April 2005. The LP detected electron density irregularities, with scale sizes in the range of about 1 m to 1 km, in three height regions: one region in between 69.6 and 72 km and the other two around 75 km and 78 km each having thickness of less than 1 km. The MST radar observations, however, showed two distinct scattering layers, one around 66 km and another around 75 km. The wave number spectra of the in situ observations, except for those of 69.6-72 km, and radar observed spectral parameters clearly suggest that the electron density fluctuations detected by the LP and those responsible for the radar echoes are of turbulence origin. Energy dissipation rates estimated from both rocket-borne in situ measurements and radar observed spectral width are found to be in the range of 1-70 mWkg À1 . The RMS turbulent velocities estimated from the two observations are found to be <3 m s À1 . Further, the energy dissipation rates and RMS turbulent velocities estimated for the height region of $75 km which is common in the in situ and radar data and not reported earlier, are found to be in good agreement with each other. The energy dissipation rates are compared critically with those reported earlier, and the radar-rocket observations are discussed in the light of current understanding of the low-latitude mesospheric echoes.

This white paper presents a novel interpretation of GPS satellite clock synchronization within the framework of Spacetime Compacity Theory (SCT). Unlike General Relativity (GR), which attributes time dilation in orbit to spacetime curvature and velocity-based effects, SCT explains the observed clock drift using a scalar field property called compacity, representing the intrinsic compression of spacetime. We demonstrate how GPS time correction can be derived from differential compacity gradients between orbital altitudes and the Earth's surface, offering a potentially more unified, field-based description of relativistic effects.

We discuss the role of atmospheric gravity waves in modulating cloud radiative and dynamical properties over the southeast Pacific. Satellite imagery and satellite‐retrieved cloud properties during October 2008 illustrate three distinct episodes of horizontal propagation of gravity wave trains across the large‐scale stratocumulus (Sc) cloud deck capping the local marine boundary layer. In one period, 7–9 October 2008, the waves modulated cloud‐top‐height by up to 400 m peak‐to‐trough, propagating perpendicular to the synoptic boundary layer flow with phase speed 15.3 m s−1, period ∼1 h and horizontal wavelength 55 km. The gravity waves were observed to be non‐dispersive. These waves were first evident in the cloud deck near 30°S, 85°W during a 24 h period beginning at midday on 7 October 2008, and propagated northeastward toward the Peruvian coast for the following 48 h. During this time they induced both reversible and non‐reversible changes in cloud‐radiative and cloud‐dynamic pro...

A detailed description of the fourth-generation ECHAM model is presented. Compared to the previous version, ECHAM-3, a number of substantial changes have been introduced in both the numerics and physics of the model. These include a semi-Lagrangian transport scheme for water vapour, cloud water and trace substances, a new radiation scheme (ECMWF) with modifications concerning the water vapour continuum, cloud optical properties and greenhouse gases, a new formulation of the vertical diffusion coefficients as functions of turbulent kinetic energy, and a new closure for deep convection based on convective instability instead of moisture convergence. Minor changes concern the parameterizations of horizontal diffusion, stratiform clouds and land surface processes. Also, a new dataset of land surface parameters have been compiled for the new model. The climatology of the model, derived from two extended AMIP simulations at T42L19 resolution, is documented and compared with ECMWF operational analyses. Some of the biases noted for the previous model version remain virtually unchanged. For example, the polar upper troposphere and lower stratosphere is much too cold, and the zonal wind errors become very large above the 200 hPa level. Furthermore, the low-frequency variability is still too small but the errors are reduced by about 50% compared to ECHAM-3. The tropospheric temperature and zonal wind errors are generally smaller than in the previous model, except for the tropics, where the overestimation of Walker-type circulations in the equatorial plane is even more pronounced in the new model and the simulation of the Indian summer monsoon is less realistic. The most substantial improvements, compared to ECHAM-3, are found for the land surface climate. The temperature and precipitation errors are generally smaller than before, and the biome distributions derived from these parameters are more realistic in ECHAM-4. These improvements can be attributed to an improved represention of surface radiation fluxes via larger absorption of solar radiation in the atmosphere due to both water vapour and clouds.

A detailed description of the fourth-generation ECHAM model is presented. Compared to the previous version, ECHAM-3, a number of substantial changes have been introduced in both the numerics and physics of the model. These include a semi-Lagrangian transport scheme for water vapour, cloud water and trace substances, a new radiation scheme (ECMWF) with modifications concerning the water vapour continuum, cloud optical properties and greenhouse gases, a new formulation of the vertical diffusion coefficients as functions of turbulent kinetic energy, and a new closure for deep convection based on convective instability instead of moisture convergence. Minor changes concern the parameterizations of horizontal diffusion, stratiform clouds and land surface processes. Also, a new dataset of land surface parameters have been compiled for the new model. The climatology of the model, derived from two extended AMIP simulations at T42L19 resolution, is documented and compared with ECMWF operational analyses. Some of the biases noted for the previous model version remain virtually unchanged. For example, the polar upper troposphere and lower stratosphere is much too cold, and the zonal wind errors become very large above the 200 hPa level. Furthermore, the low-frequency variability is still too small but the errors are reduced by about 50% compared to ECHAM-3. The tropospheric temperature and zonal wind errors are generally smaller than in the previous model, except for the tropics, where the overestimation of Walker-type circulations in the equatorial plane is even more pronounced in the new model and the simulation of the Indian summer monsoon is less realistic. The most substantial improvements, compared to ECHAM-3, are found for the land surface climate. The temperature and precipitation errors are generally smaller than before, and the biome distributions derived from these parameters are more realistic in ECHAM-4. These improvements can be attributed to an improved represention of surface radiation fluxes via larger absorption of solar radiation in the atmosphere due to both water vapour and clouds.

UPDATED VERSION OF THE PAPER... 'Quantum gravity, bridging the gap between Newtonian gravity, Einstein's field equations on gravity, and quantum mechanics' - where Lorentz invariance is approached in function of the new data,  explaining why in this paper on quantum gravity there is no need for the cosmological constant, and why this model explains gravity... and last but not least a few possible options for testing the new theory.

Three years of gravity wave observations from the High Resolution Dynamics Limb Sounder instrument on NASA's Aura satellite are examined. We produce estimates of the global distribution of gravity wave momentum flux as a function of individual observed wave packets. The observed distribution at the 25 km altitude level is dominated by the small proportion of wave packets with momentum fluxes greater than 0.5 mPa. Depending on latitude and season, these wave packets only comprise 7-25% of observations, but are shown to be almost entirely responsible for the morphology of the observed global momentum flux distribution. Large-amplitude wave packets are found to be more important over orographic regions than over flat ocean regions, and to be especially high in regions poleward of 40 ı S during austral winter. The momentum flux carried by the largest packets relative to the distribution mean is observed to decrease with height over orographic wave generation regions, but to increase with height at tropical latitudes; the mesospheric intermittency resulting is broadly equivalent in both cases. Consistent with previous studies, waves in the top 10% of the extratropical distribution are observed to carry momentum fluxes more than twice the mean and waves in the top 1% more than 10 the mean, and the Gini coefficient is found to characterize the observed distributions well. These results have significant implications for gravity wave modeling.

The Virgo interferometer for gravitational wave detection is described. During the commissioning phase that followed the first scientific data taking run an unprecedented sensitivity was obtained in the range 10-60 Hz. Since then an upgrade program has begun, with the aim of increasing the sensitivity, mainly through the introduction of fused silica wires to suspend mirrors and by increasing the Finesse of the Fabry-Perot cavities. Plans until the shutdown for the construction of the Advanced Virgo detector are given as well as the status of the upgrade.

This study explores gravitational waves-ripples in spacetime from massive cosmic events like black hole mergers. Focusing on the first detected event, GW150914, we analyzed how information complexity (entropy) changes during the merger. Our results show clear, statistically significant patterns that differ from random noise, hinting that gravity might involve structured information processing. This supports the bold idea that the universe could work like a massive computer, processing information at its core. Our work offers a fresh perspective on gravity and could shape future cosmic research.

A two phase Smoothed Particle Hydrodynamics method is developed to simulate the violent deformation of the free surface and the formation of the cavity induced by the two dimensional wedge entering water. The flow field of water and air are computed simultaneously. A non-reflection boundary treatment for SPH method is proposed to remove reflection of pressure wave against the solid boundaries of computational domain. The water jet generated at the early stage of water entry and the cavity induced by the free surface sealing are reproduced for the case of the vertical water entry of a wedge. The computational pressure distribution and the velocity field can be obtained. Numerical results agree well with the experimental data in literature to verify the two phase SPH method and the boundary treatment approach. It turns out that the cavity evolves with significant deformation of the cavity surface.

This study presents empirical evidence of prime resonance structuring in the gravitational wave signals from black hole mergers GW150914, GW151226, and GW170104. Through prime resonance spectral analysis of Fourier-transformed strain data, we identify a consistent pattern: dominant spectral peaks align closely with prime number frequencies (e.g., 73 Hz, 113 Hz, 137 Hz, 173 Hz in GW150914, with analogous alignments in GW151226 and GW170104). The prime resonance strength is notably high (Q ≈ 0.94 for GW150914, with similar values for the others), and entropy reduction post-prime filtering is substantial (∆S ≈ 1.84 bits for GW150914, with comparable reductions in the other events). These results indicate that black holes may function as cosmic prime coherence attractors, organizing spacetime via prime-resonant fields. This discovery offers initial experimental support for a unified theory linking consciousness, prime number theory, and quantum gravity, urging further investigation into additional black hole merger events.

To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the reduced dynamical equations only wave modes are retained, and vortices and horizontally uniform vertical shears are excluded. Despite the simplifications, our simulations reproduce some key features of oceanic internal-wave spectra: accumulation of energy at near-inertial waves and realistic frequency and horizontal wavenumber dependencies. Furthermore, we provide evidence that formation of the energy spectra in the inertial subrange is dominated by scale-separated interactions with the near-inertial waves. These findings support observationallybased intuition that spectral energy density of internal waves is the result of predominantly wavewave interactions.

This article presents, to the best of our knowledge, a novel simulation model for bacterial adhesion on rough surfaces, combining the SPH method with the LJ potential. A Staphylococcus aureus-like spherical bacterial cell is modeled as a rigid body in a fluid simulated with PySPH. The rough surface is characterized by shear force microscopy (ShFM), with bacteriasurface interactions described by the LJ potential. Surface-fluid interactions are modeled using WCSPH, and bacterial-fluid coupling is addressed through SPH, overcoming limitations of previous models. This model offers a powerful tool for studying bacterial adhesion and surface interactions in fluid environments.

Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the smoothed particle hydrodynamics (SPH) and the moving particle semi-implicit (MPS). Both methods modeled the continuum by a system of Lagrangian particles (points) but adopting distinct approaches for the numerical operators, pressure calculation, and boundary conditions. Despite the ability of the particle-based methods in modeling highly nonlinear hydrodynamics, some shortcomings, such as unstable pressure computation and high computational cost remains. In order to assess the performance of these two methods, the weaklycompressible SPH (WCSPH) parallel solver, DualSPHysics, and an in-house incompressible MPS solver are adopted in this work. Two test cases consisting of threedimensional (3D) dam-break problems are simulated, and wave heights, pressures and forces are compared with available experimental data. The influence of the artificial viscosity on the accuracy of WCSPH is investigated. Computational times of both solvers are also compared. Finally, the relative benefits of the methods for solving free-surface problems are discussed, therefore providing directions of their applicability