arXiv Physics @arxiv_physics@qoto.org

As part of a new approach to calculating the total energy of a diatomic molecule (cluster), it is shown that in the first order of perturbation theory, the total energy of a triatomic cluster is equal to the sum of the total energies of the diatomic clusters (molecules). If all three aluminum atoms are in the ground state of Al(2p), then the quantum of energy of collective electron oscillations (plasmon energy) in each of the diatomic clusters (molecules) is eV (electron volts).

An exact solution for the motion in time of the swinging Atwood machine is presented. The trajectories of the so called teardrop-heart orbits are obtained considering an extended Hamiltonian and a time transformation first introduced by Poincare. The motion is isochronous with respect to the launch angle.

Road traffic simulations are crucial for establishing safe and efficient traffic environments. They are used to test various road applications before real-world implementation. SUMO is a well-known simulator for road networks and intermodal traffic, often used in conjunction with other tools to test various types of applications. Realistic simulations require accurate movement models for different road users, such as cars, bicycles, and buses. While realistic models are already implemented for most vehicle types, bicycles, which are essential for achieving safe and efficient traffic, can only be modeled as slow vehicles or fast pedestrians at present. This paper introduces the Realistic Bicycle Dynamics Model (RBDM), the first dedicated bicycle model for SUMO, addressing this significant gap. Leveraging real-world bicycle data from the SimRa dataset, the RBDM implements realistic speed, acceleration, and deceleration behaviors of bicycles in urban scenarios. The evaluation is conducted using the Monaco SUMO traffic scenario and a newly generated Berlin scenario in SUMO. The RBDM significantly outperforms the existing slow-vehicle approximation in SUMO, aligning more closely with real-world data. These results underscore the necessity of a realistic bicycle movement model for accurate simulations, given the significant differences in the movement profiles of bicycles, cars, and pedestrians. Furthermore, the model is tested for its ability to generalize to disparate scenarios and urban topologies, which is dependent on the manner and geographical region in which the SimRa data were gathered. In addition, recommendations are provided for how it could be adapted for use in different city topologies.

The study guide (textbook) is part of a set of materials designed to support high-quality practical training in physics. It includes a collection of tasks for organizing both in-class and independent work. The guide serves as a foundation for further study in physics-related disciplines and aligns with current educational programs. This textbook presents a curated set of 120 physics problems with detailed solutions, structured according to the first-year bachelor's curriculum. Each section addresses common student questions and emphasizes conceptual understanding. Problem-solving is essential in physics education. It not only tests knowledge but also transforms theory into practical skills. Applying physical laws to real-world scenarios enhances comprehension and fosters analytical thinking. Through solving problems, students gain deeper insight into physical phenomena and develop effective strategies for analysis, and develop solutions to tasks-making the learning process truly comprehensive.

Many modern countries have not learned their lessons and often hope for the wisdom of later generations, resulting in them only possessing modern technology and difficult to iterate ancient civilizations. At present, there is no way to tell how we should learn from history and promote the gradual upgrading of civilization. Therefore, we must tell the history of civilization's progress and the means of governance, learn from experience to improve the comprehensive strength and survival ability of civilization, and achieve an optimal solution for the tempering brought by conflicts and the reduction of internal conflicts. Firstly, we must follow the footsteps of history and explore the reasons for the long-term stability of each country in conflict, including providing economic benefits to the people and means of suppressing them; then, use mathematical methods to demonstrate how we can achieve the optimal solution at the current stage. After analysis, we can conclude that the civilization transformed from human plowing to horse plowing can easily suppress the resistance of the people and provide them with the ability to resist; The selection of rulers should consider multiple institutional aspects, such as exams, elections, and drawing lots; Economic development follows a lognormal distribution and can be adjusted by expected value and variance. Using a lognormal distribution with the maximum value to divide equity can adjust the wealth gap.

The rapid expansion of biomolecular datasets presents significant challenges for computational biology. Quantum computing emerges as a promising solution to address these complexities. This study introduces a novel quantum framework for analyzing TART-T and TART-C gene data by integrating genomic and structural information. Leveraging a Quantum Neural Network (QNN), we classify hotspot mutations, utilizing quantum superposition to uncover intricate relationships within the data. Additionally, a Variational Quantum Eigensolver (VQE) is employed to estimate molecular ground-state energies through a hybrid classical-quantum approach, overcoming the limitations of traditional computational methods. Implemented using IBM Qiskit, our framework demonstrates high accuracy in both mutation classification and energy estimation on current Noisy Intermediate-Scale Quantum (NISQ) devices. These results underscore the potential of quantum computing to advance the understanding of gene function and protein structure. Furthermore, this research serves as a foundational blueprint for extending quantum computational methods to other genes and biological systems, highlighting their synergy with classical approaches and paving the way for breakthroughs in drug discovery and personalized medicine.

This paper studies brachistochrone trajectories. Four rules are formulated as sufficient conditions. Two rules apply for a general conservative force. Two rules apply for a central force. A central force allows wire replacement. The wire is replaced by appropriate magnetic field. This enables solving motion equations directly. We replace Euler Lagrange with direct integration.

As an alternative to the ultraviolet light emitting diode(UV LED), the feasibility of utilizing UV micro-LED in the charge management in the detection of gravitational waves in space is experimentally studied. Compared with UV LED, micro-LED is more compact in size, has better current spreading, faster response time and longer operating life. Performance characteristics of micro-LEDs were measured, with peak wavelength of 254 nm, 262 nm, 274 nm, and 282 nm for each respective micro-LED, and the photoelectric effect was demonstrated. The effectiveness of micro-LED based charge management experiments were demonstrated using above micro-LEDs mounted on a cubical test mass, and different discharge rates were achieved by varying the drive current and duty cycle using pulse width modulation(PWM). Laboratory data was also shown to demonstrate the space qualification of the micro-LED device, the key electrical and optical characteristics of the micro-LEDs showed less than 5% variation. The results of the qualification bring the micro-LED device Technology Readiness Level(TRL) to TRL-5. TRL-6 will be reached provided additional radiation and thermal tests are conducted and in a position ready to be flown and further tested in space.

Humans increasingly rely on large language models (LLMs) to support decisions in social settings. Previous work suggests that such tools shape people's moral and political judgements. However, the long-term implications of LLM-based social decision-making remain unknown. How will human cooperation be affected when the assessment of social interactions relies on language models? This is a pressing question, as human cooperation is often driven by indirect reciprocity, reputations, and the capacity to judge interactions of others. Here, we assess how state-of-the-art LLMs judge cooperative actions. We provide 21 different LLMs with an extensive set of examples where individuals cooperate -- or refuse cooperating -- in a range of social contexts, and ask how these interactions should be judged. Furthermore, through an evolutionary game-theoretical model, we evaluate cooperation dynamics in populations where the extracted LLM-driven judgements prevail, assessing the long-term impact of LLMs on human prosociality. We observe a remarkable agreement in evaluating cooperation against good opponents. On the other hand, we notice within- and between-model variance when judging cooperation with ill-reputed individuals. We show that the differences revealed between models can significantly impact the prevalence of cooperation. Finally, we test prompts to steer LLM norms, showing that such interventions can shape LLM judgements, particularly through goal-oriented prompts. Our research connects LLM-based advices and long-term social dynamics, and highlights the need to carefully align LLM norms in order to preserve human cooperation.

The issue of whether we make decisions freely has vexed philosophers for millennia, Resolving this is vital for solving a diverse range of problems, from the physiology of how the brain makes decisions (and how we assign moral responsibility to those decisions) to the interpretation of experiments on entangled quantum particles. A deterministic model of free will is developed, based on two concepts. The first generalises the notion of initialisation of nonlinear systems where information cascades upscale from the Planck scale, exemplified by the chaology of colliding billiard balls, and featured in the author's Rational Quantum Mechanics. With `just-in-time' initialisation, such Planck-scale information is only initialised when it is needed to describe super-Planck scale evolution, and not e.g., at the time of the Big Bang. In this way determinism does not imply predestination and a system with finitely many degrees of freedom can shadow a system with infinitely many, over arbitrarily long timescales. The second concept describes the upscale control of such Planck-scale information on super-Planck scales and is illustrated by reference to stochastic rounding in numerical analysis. Using these concepts, a deterministic model is proposed whereby freely-made decisions are made by using past experiences to control the impact of noise in the low-energy brain. It is claimed that such a model has evolutionary advantages, not least preventing paralysis by analysis and encouraging rational risk taking. It is concluded that humans have free will, determinism notwithstanding. The model is applied to study the foundational issue of free choice in quantum physics experiments: it is shown that violating the Measurement Independence assumption does not invalidate the free-will conclusion above.

We have developed a machine-learning potential that accurately models the behavior of iron under the conditions of Earth's core. By performing numerous nanosecond scale equilibrium molecular dynamics simulations, the viscosities of liquid iron for the whole outer core conditions are obtained with much less uncertainty. We find that the Einstein-Stokes relation is not accurate for outer core conditions. The viscosity is on the order of 10s \si{mPa.s}, in agreement with previous first-principles results. We present a viscosity map as a function of pressure and temperature for liquid iron useful for geophysical modeling.

The Looping pendulum phenomenon was first introduced in 2019 at the 32nd edition of the IYPT, wherein a lighter bob sweeps around a cylindrical rod to support the weight of a heavier bob. In this paper, the phenomenon was divided based on rotating and non-rotating forces, and differential equations were derived for each. To verify the theoretical derivation, an experimental analysis was done, varying the mass ratio with the vertical distance travelled by the heavier bob. (Tracked using tracker) Experimental findings fit a logarithmic curve fit -- falling succinctly with a similar trend with the simulation run with MATLAB solving the derived differential equations. Furthermore, to verify the simulation, the trajectory of both the lighter and heavier mass was also compared for the simulation and experimental findings. The experimental findings fit very closely to the simulation findings, accrediting the validity and accuracy of the derived theory.

The limitations of digital electronics in handling real-time matrix operations for emerging computational tasks - such as artificial intelligence, drug design, and medical imaging - have prompted renewed interest in analog computing. Programmable Integrated Photonics (PIP) has emerged as a promising technology for scalable, low-power, and high-bandwidth analog computation. While prior work has explored PIP implementations of quantum and neuromorphic computing, both approaches face significant limitations due to misalignments between their mathematical models and the native capabilities of photonic hardware. Building on the recently proposed Analog Programmable-Photonic Computation (APC) - a computation theory explicitly matched to the technological features of PIP - we introduce its critical missing component: an information theory. We present Analog Programmable-Photonic Information (API), a mathematical framework that addresses fundamental concepts beyond APC by examining the amount of information that can be generated, computed and recovered in a PIP platform. API also demonstrates the robustness of APC against errors arising from system noise and hardware imperfections, enabling scalable computation without the extensive error-correction overhead required in quantum computing. Together, APC and API provide a unified foundation for on-chip photonic computing, offering a complementary alternative to digital, quantum and neuromorphic paradigms, and positioning PIP as a cornerstone technology for next-generation information processing.

Integrated photonic devices that can be co-packaged with electronics and can operate in real-world environments will enable many important applications, such as optical interconnects, quantum information processing, precision measurements, spectroscopy, and microwave generation. Significant progress has been made over the past two decades on increasing the functional complexity of photonic chips. However, the most critical challenge that remains is the lack of scalable techniques to overcome perturbations arising from environmental thermal noise and thermal crosstalk from co-packaged electronics and other photonic devices sharing the same substrate. Here, we propose and demonstrate a fully-integrated scheme to monitor and stabilize the temperature of a high-Q microresonator in a Si-based chip. We show that when stabilized, the microresonator exhibits remarkable resilience against external thermal noise and can serve as a fully-integrated photonic frequency reference. By simply changing the temperature set-point, the cavity resonance frequency can be repeatably tuned without any hysteresis over several hours. We also show that the frequency of a distributed feedback (DFB) laser can be stabilized to this microresonator and realize a 48 dB reduction in its frequency drift, resulting in its center wavelength staying within +-0.5 pm of the mean over the duration of 50 hours in the presence of significant ambient fluctuations. This performance is superior to many commercial DFB systems and is highly suitable for use in data-communication systems. Finally, we demonstrate that the technique can be implemented to stabilize a soliton modelocked Kerr comb against significant ambient and crosstalk thermal noise, without the need for photodetection, paving the way for Kerr-comb-based photonic devices that can operate in the desired modelocked state indefinitely.

An economic modeling approach for cavity quantum electrodynamics is provided by mean-field dynamics, wherein the optical field is described classically while a self-consistent interaction with quantum emitters is incorporated through the Ehrenfest theorem. However, conventional implementations of mean-field dynamics are known to suffer from a catastrophic leakage of zero-point energy, to lose accuracy in the short-cavity limit, and to require large numbers of trajectories to be sampled. Here, we address these three shortcomings within a single integrated approach. This approach builds on our recently-proposed modification of the Ehrenfest theorem, referred to as decoupled mean-field (DC-MF) dynamics, in combination with a focused sampling scheme that enforces zero-point energy at the single-trajectory level. The approach is shown to yield high accuracy in both short and long-cavity limits while reaching convergence within a minimal amount of trajectories.

Our study found that integrating shear piezo-transducers inside the beam offers a compact and efficient solution that enables localized damping control without compromising structural integrity. However, the conventional approach of placing the piezos outside the substrate faces challenges and limited accessibility to industrial applications. We determine damping performance for long and slender sandwich beam structures utilizing active vibration control by internally placed piezoelectric shear sensors and actuators. Experimental and numerical results are presented for a clamped-free sandwich beam structure constructed with two stainless steel facings composed of a core layer of foam and a piezoelectric shear-actuator and sensor. This approach of internal actuator and sensor tends to tackle the problems within (high-tech) systems, i.e. mechanical vibrations, a limited amount of design volume, and vulnerability of externally placed piezoelectric transducers to outside conditions. By this new internal sensor-actuator approach, this study addresses a significant gap in the literature. The location of the sensor and actuator has been defined by numerical investigation of the \textit{modal shear strain} and the \textit{effective electro-mechanical coupling coefficient}. The frequency response of the sandwich beam structure has been evaluated using both numerical and experimental investigation. Positive Position Feedback has been employed on the numerical response to simulate the damping performance for the fundamental mode. Different controller gains have been used to analyze the trade-off between effective resonance suppression and increased low-frequency gain. The tip vibrations at the fundamental mode have been reduced from 5.01 mm to 0.34 mm amplitude at steady state, which represents a significant reduction.

Simulating showers of particles in highly-granular calorimeters is a key frontier in the application of machine learning to particle physics. Achieving high accuracy and speed with generative machine learning models can enable them to augment traditional simulations and alleviate a major computing constraint. Recent developments have shown how diffusion based generative shower simulation approaches that do not rely on a fixed structure, but instead generate geometry-independent point clouds, are very efficient. We present a transformer-based extension to previous architectures which were developed for simulating electromagnetic showers in the highly granular electromagnetic calorimeter of the International Large Detector, ILD. The attention mechanism now allows us to generate complex hadronic showers with more pronounced substructure across both the electromagnetic and hadronic calorimeters. This is the first time that machine learning methods are used to holistically generate showers across the electromagnetic and hadronic calorimeter in highly granular imaging calorimeter systems.

Metasurfaces are ultra-thin optical elements composed of engineered sub-wavelength structures that enable precise control of light. Their inverse design - determining a geometry that yields a desired optical response - is challenging due to the complex, nonlinear relationship between structure and optical properties. This often requires expert tuning, is prone to local minima, and involves significant computational overhead. In this work, we address these challenges by integrating the generative capabilities of diffusion models into computational design workflows. Using an RCWA simulator, we generate training data consisting of metasurface geometries and their corresponding far-field scattering patterns. We then train a conditional diffusion model to predict meta-atom geometry and height from a target spatial power distribution at a specified wavelength, sampled from a continuous supported band. Once trained, the model can generate metasurfaces with low error, either directly using RCWA-guided posterior sampling or by serving as an initializer for traditional optimization methods. We demonstrate our approach on the design of a spatially uniform intensity splitter and a polarization beam splitter, both produced with low error in under 30 minutes. To support further research in data-driven metasurface design, we publicly release our code and datasets.

One of the common tasks required for designing new plasma scenarios or evaluating capabilities of a tokamak is to design the desired equilibria using a Grad-Shafranov (GS) equilibrium solver. However, most standard equilibrium solvers are time-independent and do not include dynamic effects such as plasma current flux consumption, induced vessel currents, or voltage constraints. Another class of tools, plasma equilibrium evolution simulators, do include time-dependent effects. These are generally structured to solve the forward problem of evolving the plasma equilibrium given feedback-controlled voltages. In this work, we introduce GSPulse, a novel algorithm for equilibrium trajectory optimization, that is more akin to a pulse planner than a pulse simulator. GSPulse includes time-dependent effects and solves the inverse problem: given a user-specified set of target equilibrium shapes, as well as limits on the coil currents and voltages, the optimizer returns trajectories of the voltages, currents, and achievable equilibria. This task is useful for scoping performance of a tokamak and exploring the space of achievable pulses. The computed equilibria satisfy both Grad-Shafranov force balance and axisymmetric circuit dynamics. The optimization is performed by restructuring the free-boundary equilibrium evolution (FBEE) equations into a form where it is computationally efficient to optimize the entire dynamic sequence. GSPulse can solve for hundreds of equilibria simultaneously within a few minutes. GSPulse has been validated against NSTX-U and MAST-U experiments and against SPARC feedback control simulations, and is being used to perform scenario design for SPARC. The computed trajectories can be used as feedforward inputs to inform and improve feedback performance. The code for GSPulse is available open-source at https://github.com/jwai-cfs/GSPulse_public.