Theoretical Threshold Research Articles

Solubility-controlled early age hydration of carbonate-activated slag: Underlying mechanisms and acceleration via seeding

The low environmental impacts and good performance of carbonate-activated binders have attracted substantial interest, while their intrinsically delayed reaction and prolonged setting times constrain widespread implementation. This study aims to investigate the early-age reaction kinetics of carbonate-activated binders, elucidate the underlying mechanisms and propose controlling methods. Results reveal that hydrotalcite and C-A-S-H gel precursors rapidly reach supersaturation within hours, yet precipitation of these phases remains absent. This phenomenon, coupled with high Si/Ca ratios in the pore solution, exhibits characteristics that may contribute to the observed reaction delays. A prolonged induction period and lethargic strength development are observed owing to the lack of strength-giving phases. The hydrotalcite and C-A-S-H concentrations surpass their theoretical solubility thresholds due to rising ionic strength and salt-in effects. The addition of a pH-neutral layered double hydroxide salt accelerates the reaction, confirming seeding impacts control pore solution saturation limits, constituting the underlying accelerator mechanism.

Glaciation of mixed-phase clouds: insights from bulk model and bin-microphysics large-eddy simulation informed by laboratory experiment

Abstract. Mixed-phase clouds affect precipitation and radiation differently from liquid and ice clouds, posing greater challenges to their representation in numerical simulations. Recent laboratory experiments using the Pi Cloud Chamber explored cloud glaciation conditions based on increased injection of ice-nucleating particles. In this study, we use two approaches to reproduce the results of the laboratory experiments: a bulk scalar mixing model and large-eddy simulation (LES) with bin microphysics. The first approach assumes a well-mixed domain to provide an efficient assessment of the mean cloud properties for a wide range of conditions. The second approach resolves the energy-carrying turbulence, the particle size distribution, and their spatial distribution to provide more details. These modeling approaches enable a separate and detailed examination of liquid and ice properties, which is challenging in the laboratory. Both approaches demonstrate that, with an increased ice number concentration, the flow and microphysical properties exhibit the same changes in trends. Additionally, both approaches show that the ice integral radius reaches the theoretical glaciation threshold when the cloud is subsaturated with respect to liquid water. The main difference between the results of the two approaches is that the bulk model allows for the complete glaciation of the cloud. However, LES reveals that, in a dynamic system, the cloud is not completely glaciated as liquid water droplets are continuously produced near the warm lower boundary and subsequently mixed into the chamber interior. These results highlight the importance of the ice mass fraction in distinguishing the mixed-phase clouds and ice clouds.

Mechanistic insight into the kinetic fragmentation of norpinonic acid in the gas phase: an experimental and density functional theory (DFT) study

Abstract. Norpinonic acid has been known as an important α-pinene atmospheric secondary organic aerosol (SOA) component. It is formed in the reaction of α-pinene, β-pinene or verbenone with atmospheric oxidizing reagents. In the presented study, tandem mass spectrometry techniques were used to determine the exact norpinonic acid fragmentation pathway in the gas phase. The precursor anion – deprotonated norpinonic acid (m/z 169), generated in an electrospray (ESI) source – was introduced into the collision cell of the mass spectrometer and fragmented using the energy-resolved collision-induced dissociation (ER-CID) technique. The experimental energy values of degradation processes were determined via analysis of the breakdown curves. Quantum chemical calculations of the reaction models were also constructed, including calculation of all transition states. Comparison between the experimental and the theoretical threshold energies calculated at a ωB97XD/6-311+G(2d,p) theoretical level has shown a good correlation. Two basic pathways of the fragmentation of the parent anion [M-H]− (m/z 169) were observed. Firstly this leads to the decarboxylation product (m/z 125) and secondly to the loss of a neutral molecule (C4H6O), together with the formation of the anion m/z 99. On the other hand, the breakdown of the anion m/z 125 gives rise to the m/z 69, 57 and 55 ions. To confirm structures formed during ER-CID experiments, the gas-phase proton transfer reactions were examined of all norpinonic acid anionic fragments with a series of neutral reagents, characterized by proton affinity (PA) values. Based on PA difference analysis, the most possible chemical structures were proposed for the observed fragment anions.

Plasmon-enhanced sub-Debye-length nanogap photoelectrochemical cells for field-assisted electrolyte-free water splitting

This work studies pure water splitting (i.e., no additional electrolyte) using plasmonic sub-Debye-length nanogap photoelectrochemical cells (NPECs). With 60 nm Au gratings covered by 4 nm amorphous TiO2 under 638 nm normal incident illumination, we demonstrate up to 66 × higher photocurrent at 1.5 V than that of Au-gratings-only NPECs. In addition, we are able to efficiently drive pure water splitting at voltages as low as 1.3 V, which is very close to the theoretical thermodynamic potential threshold of 1.23 V. Our electromagnetic finite difference time domain (FDTD) simulation results (Lumerical Inc.) show a 240 × increase in the electric field intensity near the TiO2 layer compared to the incident electric field. We attribute our observations to 1) Hot spots generated by surface plasmonic resonance (SPR) on Au gratings, which greatly increase the number of electron-hole pairs; 2) The 60 nm gap distance between electrodes, which is smaller than the Debye length of pure water (∼220 nm) resulting in a much higher electric field by eliminating the shield effect and by coupling two half-reactions of water splitting together; and 3) The 4 nm amorphous TiO2, which improves hot carriers separation. Our NPEC is a promising device for efficient hydrogen production enabling the utilization of visible light.

Performance Analysis of an Aerial Remote Sensing Platform Based on Real-Time Satellite Communication and Its Application in Natural Disaster Emergency Response

The frequency of natural disasters has increased recently, posing a huge threat to human society. Rapid, accurate, authentic, and comprehensive acquisition and transmission of disaster information are crucial in emergency response. In this paper, we propose a design scheme for an aerial remote sensing platform based on real-time satellite communication. This platform mainly includes a civilian heavy-duty unmanned aerial vehicle, ground observation system with the self-developed orthographic image stabilization device, wireless communication system with an airborne mobile communication device using Ku band, ground satellite information receiving station, and data processing and application analysis system. The image stabilization capability of the ground observation system and the communication capability of the wireless communication system were verified through ground and flight tests respectively. The results showed that the stability accuracy of the platform was better than the theoretical threshold, the system transmission rate was not less than 2 M bandwidth, the data packet loss rate was low, and the time delay was not more than 2 s. The images captured in the experiment were clear, with a resolution of less than 1cm and an overlap rate of more than 70%. These all results meet the emergency observation requirement, which indicates that the aerial remote sensing platform based on real-time satellite communication has great potential for application in natural disaster emergency response.

Prostate radiotherapy may cause fertility issues: a retrospective analysis of testicular dose following modern radiotherapy techniques

BackgroundProstate cancer in younger men is rare but not exceptional. Radiotherapy is a cornerstone of prostate cancer treatment and yet, its impact on fertility is scarcely reported in literature. Given the radiosensitivity of testicular tissue, this study aimed to determine the testicular dose using modern radiotherapy techniques for definitive prostate irradiation.MethodsOne hundred radiotherapy plans were reviewed. Testicles were contoured retrospectively without dosimetric optimization on testicles.ResultsThe median testicular dose was 0.58 Gy: 0.18 Gy in stereotactic plans, 0.62 Gy in Volumetric Modulated Arc Therapy plans and 1.50 Gy in Tomotherapy plans (p < 0.001). Pelvic nodal irradiation increased the median testicular dose to 1.18 Gy versus 0.26 Gy without nodal irradiation (p < 0.001). Weight and BMI were inversely associated with testicular dose (p < 0.005). 65% of patients reached the theoretical dose threshold for transient azoospermia, and 10% received more than 2 Gy, likely causing definitive azoospermia.ConclusionDespite being probably lower than doses from older techniques, the testicular dose delivered with modern prostate radiotherapy is not negligible and is often underestimated because the contribution of daily repositioning imaging is not taken into account and most Treatment Planning Systems underestimate the out of field dose. Radiation oncologists should consider the impact on fertility and gonadal endocrine function, counseling men on sperm preservation if they wish to maintain fertility.Trial registration: retrospectively registered.

Compositional nutrient analysis of greenhouse grown ryegrass (Lolium multiforum) fertilized with raw and hydrothermal-treated igneous rock as diagnostic tool for balanced fertilization in tropical environments

Due to the escalating demand for conventional potassium sources, and their unavailability in many African countries, there is a growing interest in hydrothermally treated igneous rocks as viable alternatives. These materials exhibit promising potential in enhancing potassium release, comparable to traditional sources like muriate of potash (M.O.P.). However, it remains uncertain whether they can adequately fulfill the nutrient requirements of plants. In this study, we evaluated nutrient balance in ryegrass (Lolium multiflorum) using raw and hydrothermally treated K-bearing silicate rocks as fertilizers. The Compositional Nutrient Diagnostic (CND) approach was used to assess the plants’ nutrient status, involving identification of high-yield subpopulations, and setting a yield cutoff. We derived a theoretical threshold for nutrient imbalance (CNDr2) using statistical methods like the chi-square distribution function and low-yield subpopulation proportion. CNDr2 was validated via Cate–Nelson partition and sum of squared individual nutrient indexes. Results showed a yield cutoff of 37.759 kg ha−1, distinguishing low-yield and high-yield subpopulations based on cumulative variance ratio functions from survey data. The theoretical threshold derived using the chi-square function was 10.1, subsequently validated by the Cate–Nelson method. Critical CND nutrient indices were symmetrical around zero, but their sum indicated foliar nutrient imbalance, notably zinc, potassium, and copper excess, attributed to 20 interactions identified (4 synergetic and 16 antagonistic). This study underscores hydrothermal treatment’s efficacy in improving nutrient availability and achieving a balanced nutrient profile compared to raw materials. It offers a promising solution for enhancing agricultural productivity, especially in tropical regions like Africa, where traditional sources are scarce.

The influence of oral contraceptives on the exercise pressor reflex in the upper and lower body.

Previous research has demonstrated that oral contraceptive (OC) users have enhanced cardiorespiratory responses to arm metaboreflex activation (i.e., postexercise circulatory occlusion, PECO) and attenuated pressor responses to leg passive movement (PM) compared to non-OC users (NOC). We investigated the cardiorespiratory responses to arm or leg metaboreflexand mechanoreflex activation in 32 women (OC, n = 16; NOC, n = 16) performing four trials: 40% handgrip or 80% plantarflexion followed by PECO and arm or leg PM. OC and NOC increased mean arterial pressure (MAP) similarly during handgrip, plantarflexion and arm/leg PECO compared to baseline. Despite increased ventilation (VE) during exercise, none of the women exhibited higher VE during arm or leg PECO. OC and NOC similarly increased MAP and VE during arm or leg PM compared to baseline. Therefore, OC and NOC were similar across pressor and ventilatory responses to arm or leg metaboreflexand mechanoreflex activation. However, some differences due to OC may have been masked by disparities in muscle strength. Since women increase VE during exercise, we suggest that while women do not display a ventilatory response to metaboreflex activation (perhaps due to not reaching a theoretical metabolite threshold to stimulate VE), the mechanoreflex may drive VE during exercise in women.

Optimizing information-driven awareness allocation for controlling activity-triggered epidemic spread

In the contemporary era, the advent of epidemics instigates a substantial upswing in relevant information dissemination, bolstering individuals’ resistance to infection by concurrently reducing activity contacts and reinforcing personal protective measures. To elucidate this intricate dynamics, we introduce a composite four-layer network model designed to capture the interplay among information-driven awareness, human activity, and epidemic spread, with a focus on the allocation of individuals’ limited attention in diminishing activity frequency and self-infection rates. One intriguing observation from our findings is an anomalous, concave non-monotonic relationship between awareness trade-off and epidemic spread, with a more pronounced prevalence at an intermediate least awareness efficacy. This underscores the inadvisability of relaxing self-protection through reduced activity frequency or compensating for increased activity frequency by enhancing self-protection. Especially noteworthy is the significance of enhancing self-protection in response to heightened information dissemination and inherent activity demands to curtail infection risk. However, in scenarios with increasing ancillary activity frequency, the emphasis should exclusively shift towards reducing activity exposure. The model establishes a theoretical threshold for accurately predicting awareness efficacy in epidemic outbreaks. Optimal awareness allocation consistently resides at the extremes—either completely avoiding unnecessary activity contact or adopting full self-protection. This guidance, contingent on information level and activity demand, offers valuable insights into the delicate balance between individual behaviors and epidemic prevention.

Dynamic navigation: Integrating GL-STGCNN and MPC for collision avoidance with future Awareness

Existing ship dynamic collision avoidance methods mostly rely on the instantaneous motion information of surrounding ships to make decisions. This makes it difficult to adapt to changes in the motion states of surrounding ships, which may lead to collisions between ships. To improve the safety of dynamic collision avoidance methods, this paper combines the multi-ship trajectory prediction model GL-STGCNN with model predictive control for ship dynamic collision avoidance tasks. Firstly, the interaction between ships is extracted through GL-STGCNN to predict the future trajectories of surrounding ships. Then, the objective function based on the artificial potential field method and the velocity obstacle method is optimized to control the ship to complete the dynamic collision avoidance task. The performance of the dynamic collision avoidance method is verified and analyzed in the ship navigation scenario simulated by AIS data. The experiments show that the new ship dynamic collision avoidance method not only complies with the COLREGs, but also can flexibly select the collision avoidance method according to different scenarios. In addition, the theoretical collision avoidance threshold distance based on the MPC objective function shows a high degree of fit with the actual collision avoidance trigger distance observed in the simulation verification.

Estimation of electric field inside a neural spheroid by low‐frequency magnetic field exposure

AbstractExposure to time‐varying, low‐frequency and high‐intensity magnetic field (MF) induce electric field (EF) inside the human body, producing stimulus effects such as nerve fiber excitation or synaptic modulation. To measure such stimulus effects by low‐frequency MF exposure in real‐time, we developed a fluorescent recording system using optical fibers that is neither affected by the MF nor affects the MF distribution. In this study, a numerical calculation model composed of voxels with a 6.25 µm spatial resolution was developed. Using this numerical model, we evaluated the distribution of the EF generated inside three‐dimensional neuronal tissue called neural spheroid, under 50 Hz sinusoidal wave, 300 mT (root mean square) uniform MF exposure. We also investigated the influence of the optical fiber on the electric field distribution in neural spheroid. As a result, MF produced an induced EF in the neural spheroid of more than 4 V/m, well above the theoretical threshold of synaptic modulation. These results indicated that our experimental system was suitable for the evaluation of the threshold of stimulus effects using neural spheroid.

Fabrication of a novel high electrical conductivity Si3N4 matrix composite with Cu three-dimensional network structure by spark plasma sintering

Silicon nitride (Si3N4) ceramic matrix conductive composite materials have shown great promise as conductive layer materials for electrical transmission components. However, existing conductive phases struggle to form a three-dimensional (3D) interconnected network in Si3N4 matrix, resulting in poor electrical conductivity. This study proposed a spark plasma sintering (SPS) process utilizing Si3N4 as the substrate and Cu particles as the reinforcement phase to fabricate a novel electrical conductivity Si3N4/Cu composite material. The results indicated that the diffusion of Si atoms in Si3N4 facilitated the formation of copper silicide (CuiSi) interface between the two constituents during sintering, creating a strong chemical bonding for high conductivity. Simultaneously, composite materials with optimized Cu content formed a 3D interconnect network structure, providing a continuous path for electrical conduction. At Cu content of 30 vol%, the Si3N4/Cu composite exhibited a satisfying electrical conductivity of 295.37 S/m, which was 14 orders of magnitude higher than that of Si3N4. The composites also demonstrated a percolation phenomenon, with a theoretical percolation threshold of Cu particles at just 0.1 vol%, an order of magnitude lower than that of carbon reinforcement particles. Furthermore, an integrated design featuring external insulation and internal conductivity was achieved by wrapping a Si3N4 insulation layer around the conductive Si3N4/Cu composites. The fabricated insulation layer exhibited higher resistivity (1.12×1014 Ω) and a lower wear rate (1.3×10−6 mm3/N·m) compared to some contemporary insulation ceramics, while the conductive layer had a lower calorific value, making them excellent candidates for electrical transmission component materials.

Hadamard Error-Correcting Codes and Their Application in Digital Watermarking.

In communication technologies such as digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC), error-correcting codes are crucial. The Enhanced Hadamard Error-Correcting Code (EHC), which is based on 2D Hadamard Basis Images, is a novel error correction technique that is presented in this study. This technique is used to evaluate the effectiveness of the video watermarking scheme. Even with highly sophisticated embedding techniques, watermarks usually fail to resist such comprehensive attacks because of the extraordinarily high compression rate of approximately 1:200 that is frequently employed in video dissemination. It can only be used in conjunction with a sufficient error-correcting coding method. This study compares the efficacy of the well-known Reed-Solomon Code with this novel technique, the Enhanced Hadamard Error-Correcting Code (EHC), in maintaining watermarks in embedded videos. The main idea behind this newly created multidimensional Enhanced Hadamard Error-Correcting Code is to use a 1D Hadamard decoding approach on the 2D base pictures after they have been transformed into a collection of one-dimensional rows. Following that, the image is rebuilt, allowing for a more effective 2D decoding procedure. Using this technique, it is possible to exceed the theoretical error-correcting capacity threshold of ⌊dmin-12⌋ bits, where dmin is the Hamming distance. It may be possible to achieve better results by converting the 2D EHC into a 3D format. The new Enhanced Hadamard Code is used in a video watermarking coding scheme to show its viability and efficacy. The original video is broken down using a multi-level interframe wavelet transform during the video watermarking embedding process. Low-pass filtering is applied to the video stream in order to extract a certain frequency range. The watermark is subsequently incorporated using this filtered section. Either the Reed-Solomon Correcting Code or the Enhanced Hadamard Code is used to protect the watermarks. The experimental results show that EHC far outperforms the RS Code and is very resilient against severe MPEG compression.

Occurrence and seasonal variations of organophosphate flame retardants in air and dust from college microenvironments at Qingdao, China: Implications for student's exposure and risk assessment

Organophosphate flame retardants (OPFRs) are widely used as alternatives to brominated flame retardants in a variety of consumer products and their consumption has continuously increased in recent years. However, their concentrations and human exposures in indoor microenvironments, particularly in a university environment, have received limited attention. In this study, the concentrations and seasonal variations of 15 OPFRs were assessed in typical microenvironments of two universities, including dormitories, offices, public microenvironments (PMEs: classroom, dining hall, gymnasium and library), and laboratories on the northern coast of China.Analysis of the OPFRs in both air and dust samples indicated widespread distribution in college campuses. The average concentration of ∑15OPFRs in the winter (12,774.4 ng/g and 5.3 ng/m3 for dust and air, respectively) was higher than in the summer (2460.4 ng/g and 4.6 ng/m3 for dust and air, respectively). The dust and air samples collected from PMEs and laboratories exhibited higher concentrations of OPFRs, followed by offices and dormitories. An equilibrium was reached between dust and air in all collected microenvironments. The daily intakes of OPFRs were significantly lower than the reference dose. Dust ingestion was the primary intake pathway in the winter, while inhalation and dust ingestion were the main intake pathways in the summer. The non-carcinogenic hazard quotients fell within the range of 10−7–10−3 in both the summer and winter, which are below the theoretical risk threshold. For the carcinogenic risk, the LCR values ranged from 10−10 to 10−8, indicating no elevated carcinogenic risk due to TnBP, TCEP, and TDCP in indoor dust and air.

Markovian Approach for Exploring Competitive Diseases with Heterogeneity-Evidence from COVID-19 and Influenza in China.

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.

Evaluation methods of BDS-3 ground-segment defensive capability oriented to satellite navigation countermeasures

Owing to intentional interference and destructions during satellite navigation countermeasures, the security application of global navigation satellite systems (GNSS) faces immense challenges. To ensure the safe application of the GNSS in complex electromagnetic environment, the system-level defensive capability need be assessed, which can make for maintaining GNSS normal service during countering and further realizing the optimal decision. Therefore, this study used the ground control segment in the GNSS as the evaluation object, the bottom indices related to the criterion layers including service performance and station function as the key evaluation indices, and the technical requirement of each index under a secure situation as the standard, to propose the evaluation system including index system and evaluation methods for the ground-segment defensive capability. As BeiDou navigation satellite system III (BDS-3) is a global navigation satellite system independently built and operated by China, it was taken as a case for method verification. Then, BDS-3 two-way observation data between the satellite and the ground and between stations, which was collected from Beijing flight Control Center, from March 5 to 12 (2022) were selected during tests, and the results were compared with the existing standards contained in BDS open service performance standard to evaluate the system-level defensive capability. Evaluation Results of positioning accuracy and error correction ability for the BDS-3's ground stations determined through seven damage experiments with different interference strength show that: Corresponding horizontal and vertical positioning accuracy of stations under test did not exceed 1 m in the statistical period and their convergence time did not exceed the limit (30 min); thus, the ground segment of the BDS-3 has a good defensive capability. Compared to comprehensive evaluation results of the BDS-3, based on the theoretical threshold (the ground-segment threshold ≤48.40 % and the space-segment threshold ≤51.60 %), we know that its ground-segment defense (14.06 %) was worse than GPS ground-segment defense (14.43 %), whereas the ground-segment defense of the BDS/GPS integrated system (15.29 %) was best and its capability evaluation grade was strong. They indicate system's future improvements should focus more on enhancing the development scale and service efficiency of the BDS-3's ground stations in the Western Hemisphere, and reasonably promote system compatibility and interoperability while considering facility cost and operating efficiency.

Mornings with the highest non‐rainfall water during 2 years of measurements in the Negev–Ecological implications

AbstractBy providing water during the long dry rainless season, non‐rainfall water (NRW), principally dew and fog, is commonly thought to serve as an important water source for arid soil biocrusts, which require water threshold of 0.05 (for lichens) and 0.1 mm (for cyanobacteria) for growth. Such values are commonly reported in the literature. Moreover, values of &gt;0.45 mm/d (considered as the practical theoretical threshold for dew) are also reported. Following an analysis of limited (29 days) dewy mornings, it was recently reported that dew is incapable of forming on the soil surface. Being of limited scope, we therefore analyse days that yielded the highest amounts of NRW during 2 years (2021–2023) of measurements (22 days with NRW ≥0.15 mm). We conducted measurements at 1 m above ground, cobbles, rocks, and the soil surface, and compared them to the cloth‐plate method. Additionally, periodical temperature measurements were conducted, and the dewpoint temperature (Td) was calculated. Our findings indicate that (a) dew yield never surpassed 0.4 mm, (b) while the water threshold amounts were reached on the rocks and especially on the cobbles, these thresholds were seldom reached on soil (a single morning with 0.1 mm and 3 days with ≥0.05 mm), (c) in comparison to air temperatures at 0.05 m and especially at 1 m‐height above ground, surface nocturnal soil temperatures were 2–3°C warmer, thus eliminating possible vapour condensation. Our data cast doubt on values of &gt;0.45 mm reported from various deserts. Additionally, while supporting the view that NRW may provide water for the growth of rock‐dwelling lichens, NRW in the Negev does not provide the soil biocrusts with sufficient water for growth.

Satisfiability Threshold of Random Propositional S5 Theories

Modal logic S5, which isan important knowledge representation and reasoning paradigm, has been successfully applied in various artificial-intelligence-related domains. Similar to the random propositional theories in conjunctive clause form, the phase transition plays an important role in designing efficient algorithms for computing models of propositional S5 theories. In this paper, a new form of S5 formula is proposed, which fixes the number of modal operators and literals in the clauses of the formula. This form consists of reduced 3-3-S5 clauses of the form l1∨l2∨ξ, where ξ takes the form □(l3∨l4∨l5), ◊(l3∧l4∧l5), or a propositional literal, and li(1≤i≤5) is a classical literal. Moreover, it is demonstrated that any S5 formula can be translated into a set of reduced 3-3-S5 clauses while preserving its satisfiability. This work further investigates the probability of a random 3-c-S5 formula with c=1,2,3 being satisfied by random assignment. In particular, we show that the satisfiability threshold of random 3-1-S5 clauses is −ln2(1−Pd−Ps)ln78+Ps·ln34, where Ps and Pd denote the probabilities of different modal operators appearing in a clause. Preliminary experimental results on random 3-1-S5 formulas confirm this theoretical threshold.

Statistical analysis of high-frequency whistler waves at Earth's bow shock: Further support for stochastic shock drift acceleration

We statistically investigate high-frequency whistler waves (with frequencies higher than ∼10% of the local electron cyclotron frequency) at Earth's bow shock using magnetospheric multi-scale (MMS) spacecraft observations. We focus specifically on the wave power within the shock transition layer, where we expect electron acceleration via stochastic shock drift acceleration (SSDA) to occur associated with efficient pitch-angle scattering by whistler waves. We find that the wave power is positively correlated with both the Alfvén Mach number in the normal incidence frame MA and in the de Hoffmann–Teller frame MA/cos θBn. The empirical relation with MA/cos θBn is compared with the theory of SSDA that predicts a threshold wave power proportional to (MA/cos θBn)−2. The result suggests that the wave power exceeds the theoretical threshold for MA/cos θBn≳30–60, beyond which efficient electron acceleration is expected. This aligns very well with previous statistical analysis of electron acceleration at Earth's bow shock [Oka et al., Geophys. Res. Lett. 33, 5–6 (2006)]. Therefore, we consider that this study provides further support for SSDA as the mechanism of electron acceleration at Earth's bow shock. At higher-Mach-number astrophysical shocks, SSDA will be able to inject electrons into the diffusive shock acceleration process for subsequent acceleration to cosmic-ray energies.

Stochastic bifurcation and chaos study for nonlinear ship rolling motion with random excitation and delayed feedback controls

In this paper, we investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. The Itoˆ-stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. Subsequently, the stochastic stability and bifurcation behaviors of the system are analyzed. Furthermore, using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D-bifurcation and stochastic P-bifurcation. We also analyze the properties and shape changes of the system’s probability density function under different parameters through numerical simulation. It has been determined that the system exhibits stochastic bifurcation behavior, specifically P-bifurcation and D-bifurcation. The validity of the method is verified by a numerical model. The theoretical chaos threshold of the system is determined using the random Melnikov method, and the impact of delayed feedback parameters on the chaotic motion of the system is analyzed by combining the bifurcation diagram, phase portrait, and time series.