Straight Line Research Articles

Non-isochronicity on piecewise Hamiltonian differential systems with homogeneous nonlinearities

In this paper, we prove the non-isochronicity of Σ-centres for a class of planar piecewise smooth differential systems with a straight switching line, whose two sub-systems are Hamiltonian differential systems with a non-degenerated centre and only homogeneous nonlinearities. This result generalizes a classical result of non-isochronicity on the smooth Hamiltonian systems with homogeneous nonlinearities.

On the construction of the Stokes flow in a domain with cylindrical ends

Based on existence results for the Stokes operator and its solution properties in manifolds with cylindrical ends by Große et al. and Kohr et al., the Stokes flow in a three‐dimensional compact domain with circular openings through which the fluid enters and leaves through unbounded cylindrical pipes the Stokes flow is modeled as a mixed boundary value problem whereas in the cylindrical ends, the velocities and pressures are constant on every straight line in the cylindrical directions with initial values from the openings of . These values equal the velocities and pressures which are obtained from the mixed boundary values' solution in at the openings .

Parallax Effect in Microlensing Events Due to Free-floating Planets

One of the most important applications of microlensing observations is the detection of free-floating planets (FFPs). The timescale of microlensing due to FFPs (t E) is short (a few days). Discerning the annual parallax effect in observations of these short-duration events due to FFPs by one observer is barely possible, though their parallax amplitude is larger than that in common events. In microlensing events due to FFPs, the lens–source relative trajectory alters because of the observer’s motion by δ u . This deviation is a straight line as long as t E ≪ P ⊕, and its size is δ u ∝ π rel (P ⊕ is the observer’s orbital period). So, most observed microlensing events due to close FFPs have simple Paczyńsky light curves with indiscernible but important parallax. To evaluate the destructive effects of invisible parallax in such events, we simulate ∼9650 microlensing events due to FFPs with t E < 10 days that are observed only by the Nancy Grace Roman Space Telescope (Roman). We conclude that in half of these microlensing events the missing parallax alters the real light curves, changing their shape and derived properties (by Δχ 2 ≳ 100). By fitting Paczyński light curves to these affected events we evaluate the relative and dimensionless deviations in the lensing parameters from their real values (δ t E, δ ρ ⋆, ...). We conclude that around 46 FFPs that are discovered by Roman have light curves highly affected by invisible parallax with δ t E > 0.1 and δ ρ ⋆ > 0.1. Our study reveals the importance of simultaneous and dense observations of the same microlensing events viewed by Roman by other observers circling the Sun in different orbits.

Error correction method based on dual-beam laser for curved rail profile measurement

The current method of dynamic rail profile measurement involves the installation of a line-structured light sensor at the base of the train. The accuracy of this measurement is influenced by the vertical relationship between the laser plane of the light sensor and the longitudinal direction of the rail (LDR). When a train travels in a straight line, the normal of the laser plane aligns with the LDR. However, when the train curves, the angle at which its wheels connect with the rails causes the laser plane’s normal direction to deviate from the LDR, leading to measurement errors. To address this issue, we propose a method for curved rail profile measurement using a dual-beam laser to correct these errors. This method involves generating an auxiliary 3D rail reflecting the LDR and a virtual 3D rail reflecting the normal direction of the laser plane from the cross-section image of the dual-beam laser. An optimization function is then formulated to determine the optimal auxiliary plane (optimal-AP) by analyzing the alignment or intersection between the auxiliary and virtual 3D rails. Distorted contour points are projected onto the optimal-AP to rectify errors. Experiments validate the accuracy and effectiveness of this proposed method. The results show that, regardless of pitch or yaw movement between the laser plane and the LDR, the error in measuring corrected profile wear remains consistently below 0.10 millimeters, thereby meeting the accuracy standard for rail wear measurement. This approach rectifies measurement errors in curved rail profiles from a 3D perspective, ensuring accurate measurements even under complex working conditions. It also provides a valuable reference for error analysis and improving dynamic rail profile measurement accuracy.

An extended graphical solution for undrained cylindrical cavity expansion in K0‐consolidated Mohr–Coulomb soil

AbstractThis paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with . It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between and or on the specific line of . The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils.

Compensación cinética y termodinámica del pardeamiento no enzimático de zumos clarificados de limón

This paper presents a study on kinetic and thermodynamic compensation to evaluate the kinetics of non-enzymatic browning of clarified lemon juices. In a previous work, the kinetic constants of browning were presented using the evolution of the absorbance at 420 nm (A420) and luminosity (L*) for different soluble solids contents (64.6; 50; 35; 20 and 10 ºBrix) and different working temperatures (70, 80, 90 and 95 ºC). The parameters of the Arrhenius equation were obtained by fitting the kinetic constants and temperatures. The variation of lnK0 with Ea follows a linear trend, so there is kinetic compensation, with isokinetic temperature values being 126.6 ºC and 149.7 ºC for A420 and L*, respectively. The transition state equilibrium constants were determined using the Eyring equation for each soluble solids content and each temperature. The equilibrium constants were adjusted to the Van't Hoff equation and the set of pairs of estimated values for the activation enthalpy and the activation entropy also followed a straight line, which causes thermodynamic compensation, with isoequilibrium temperatures of 112.8 ºC and 136.3 ºC for A420 and L*, respectively. It was concluded that the browning mechanism is the same for the ranges of soluble solids content and temperature studied. Since all isokinetic and isoequilibrium temperatures were higher than the working temperature values, it was also concluded that the control was enthalpic for all cases. To avoid the deterioration of these juices, it is advisable to intervene in the working temperature, trying to ensure that the heat treatment is carried out at the lowest possible temperature.

Fine Cloud Structures on a Hard Snowball Earth

AbstractEarth may have been globally ice‐covered at least two times during the Cryogenian Period (720–635 Ma). Previous studies showed that clouds could strongly warm a hard snowball Earth and promote its deglaciation. However, the understanding of clouds was largely based on coarse‐resolution global simulations with parameterized convection and clouds, or high‐resolution cloud‐resolving simulations with explicit convection and clouds but limited to a small domain without the effects of large‐scale circulation. Here we present the first global non‐hydrostatic high‐resolution (30 km) simulation to investigate snowball clouds and their radiative effects. We show that spatial‐temporal cloud distributions exhibit clear meanders (patterns of curved lines rather than straight lines along the west‐east direction) and strong variabilities, which result from the tight interactions among the Inter‐Tropical Convergence Zone, Hadley cells, and baroclinic instability. The net cloud radiative effect is around 20 W m−2 in the tropics, consistent with previous global general circulation model simulations.

The 16th Hilbert Problem for Discontinuous Piecewise Linear Hamiltonian Saddles and Isochronous Centers Separated by a Straight Line

The 16th Hilbert Problem for Discontinuous Piecewise Linear Hamiltonian Saddles and Isochronous Centers Separated by a Straight Line

Finite-displacement elastic solution due to a triple contact line

At the line of triple contact of an elastic body with two immiscible fluids, the body is subjected to a force concentrated on this line, the fluid–fluid surface tension. In the simple case of a semi-infinite body, limited by a plane, a straight contact line on this plane, and a fluid–fluid surface tension normal to the plane, the classical elastic solution leads to an infinite displacement at the contact line and an infinite elastic energy. By taking into account the body–fluid surface tension (i.e., isotropic surface stress) and applying Kolosov’s approach of plane strain elasticity, we present a new and simple expression of the solution concerning the semi-infinite body, which gives a finite displacement and a ridge at the contact line, and finite elastic energy. A detailed description of the displacements, strains, and stresses in the neighborhood of the contact line is given. This solution also shows that Green’s formulae, in the volume and on the surfaces, are valid (these formulae play a central role in the theory).

Simple mathematical model for predicting COVID-19 outbreaks in Japan based on epidemic waves with a cyclical trend

BackgroundSeveral models have been used to predict outbreaks during the COVID-19 pandemic, with limited success. We developed a simple mathematical model to accurately predict future epidemic waves.MethodsWe used data from the Ministry of Health, Labour and Welfare of Japan for newly confirmed COVID-19 cases. COVID-19 case data were summarized as weekly data, and epidemic waves were visualized and identified. The periodicity of COVID-19 in each prefecture of Japan was confirmed using time-series analysis and the autocorrelation coefficient, which was used to investigate the longer-term pattern of COVID-19 cases. Outcomes using the autocorrelation coefficient were visualized via a correlogram to capture the periodicity of the data. An algorithm for a simple prediction model of the seventh COVID-19 wave in Japan comprised three steps. Step 1: machine learning techniques were used to depict the regression lines for each epidemic wave, denoting the “rising trend line”; Step 2: an exponential function with good fit was identified from data of rising straight lines up to the sixth wave, and the timing of the rise of the seventh wave and speed of its spread were calculated; Step 3: a logistic function was created using the values calculated in Step 2 as coefficients to predict the seventh wave. The accuracy of the model in predicting the seventh wave was confirmed using data up to the sixth wave.ResultsUp to March 31, 2023, the correlation coefficient value was approximately 0.5, indicating significant periodicity. The spread of COVID-19 in Japan was repeated in a cycle of approximately 140 days. Although there was a slight lag in the starting and peak times in our predicted seventh wave compared with the actual epidemic, our developed prediction model had a fairly high degree of accuracy.ConclusionOur newly developed prediction model based on the rising trend line could predict COVID-19 outbreaks up to a few months in advance with high accuracy. The findings of the present study warrant further investigation regarding application to emerging infectious diseases other than COVID-19 in which the epidemic wave has high periodicity.

Four crossing limit cycles of a family of discontinuous piecewise linear systems with three zones separated by two parallel straight lines

Four crossing limit cycles of a family of discontinuous piecewise linear systems with three zones separated by two parallel straight lines

Electrowriting patterns and electric field harness directional cell migration for skin wound healing

Directional cell migration is a crucial step in wound healing, influenced by electrical and topographic stimulations. However, the underlying mechanism and the combined effects of these two factors on cell migration remain unclear. This study explores cell migration under various combinations of guided straight line (SL) spacing, conductivity, and the relative direction of electric field (EF) and SL. Electrowriting is employed to fabricate conductive (multiwalled carbon nanotube/polycaprolactone (PCL)) and nonconductive (PCL) SL, with narrow (50 μm) and wide (400 μm) spacing that controls the topographic stimulation strength. Results show that various combinations of electrical and topographic stimulation yield significantly distinct effects on cell migration direction and speed; cells migrate fastest with the most directivity in the case of conductive, narrow-spacing SL parallel to EF. A physical model based on intercellular interactions is developed to capture the underlying mechanism of cell migration under SL and EF stimulations, in agreement with experimental observations. In vivo skin wound healing assay further confirmed that the combination of EF (1 V cm−1) and parallelly aligned conductive fibers accelerated the wound healing process. This study presents a promising approach to direct cell migration and enhance wound healing by optimizing synergistic electrical and topographic stimulations.

A new target accessibility control method based on SMC

ABSTRACT In this paper, a sliding mode control method based on improved intelligent decision (IID-SMC) algorithm is proposed to improve the accuracy of the puncture needle to reach the target and reduce the time required in the puncture process. First of all, around the straight line of the puncture needle and the direction of the rotation of the needle, the independent control law is designed to realise the mutual decoupling and reduce the mutual interference. Secondly, the error range of this method in the process of puncture is analysed, and the upper bound of the error in the process of puncture is given. Finally, the method is verified by simulation and experiment platform.

Relationships between Anthropogenic Activities and Distribution of Medium to Large Mammal Species Assemblage in Madi Wildlife Corridor: Implication for Biodiversity Conservation in Uganda

Wildlife corridors between protected areas increase connectivity by integrating populations into single demographic units, thereby increasing gene flows within populations and thus probability of survival. This study assessed the relationship between anthropogenic activities and mammal species assemblage within and around Madi wildlife corridor. The study adopted recce walks along a zig-zag line transect and straight line transect methods of game tracking. Global Position System (GPS) was used to map locations of direct mammal sightings, vocalizations, tracks, dung/droppings, diggings, carcasses, and skeletal remains of mammal species. Similarly, anthropogenic activities such as hunting using bow and arrows, rifles, trapping, tree cutting, charcoal burning, bush burning, cultivation, and settlements that seemed to influence assemblage of the mammals in the area of study were mapped. The result showed that the Madi wildlife corridor still contained diverse mammal species including but not limited to; the African Elephants (Loxodonta Africana sp.), Buffaloes (Syncerus caffer) Leopards (Panthera pardus), Spotted Hyena (Crocuta Crocuta), Northern Giraffe (Giraffa Camelopardalis), Uganda kob (Kobus kob thomasi), Hartebeest (Alcelaphus buselaphus) and Reedbuck (Redunca arundinum), which were comparable to that of the adjacent Murchison Falls National Park (MFNP). The relationship between anthropogenic activities and species assemblage showed a negatively skewed distribution of some of the large mammal species specifically Elephants, Giraffes, and Hippopotamus. The study recommends gazettement of a wildlife corridor between MFNP and East Madi Wildlife Reserve to promote wildlife connectivity between two adjacent ecosystem-protected areas in northern Uganda. As a long-term strategy for wildlife conservation, it is crucial to undertake a systematic assessment and prioritization and demarcation of wildlife corridors and development of a comprehensive action plan for securing them. We further recommend development of a national Wildlife Corridor Regulations to provide a framework for the sustainable conservation of biodiversity

Minkowski Space from Quantum Mechanics

Penrose’s Spin Geometry Theorem is extended further, from SU(2) and E(3) (Euclidean) to E(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of E(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of E(1, 3)-invariant basic observables, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for E(1, 3)-invariant elementary quantum mechanical systems in terms of the basic quantum observables in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the metric structure of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems.

TFL perforator flap – complementing and completing the ALT-AMT flap axis.

Background: Antero-lateral thigh flap (ALT) is the most common soft tissue flap used for microvascular reconstruction of head and neck. Its harvest is associated with some unpredictability due to variability in perforator characteristics, injury or unfavorable configuration for complex defects. Antero-medial thigh flap (AMT) is an option, but the low incidence and thickness restricts its utility. TFL perforator flap (TFLP) is an excellent option to complement ALT. Its perforator is consistent, robust, in vicinity and lends itself with ALT perforator, to large conjoint flap, chimeric designs and possible two free flap harvest from the same thigh. Methods: Analysis of 29 cases with a free flap for head neck reconstruction with an element of TFLP. Results: All cases were primarily planned for an ALT reconstruction. There was absence of the ALT perforator in 16 cases but a sizable TFL perforator was available. In 13 cases the complex defect warranted use of both ALT plus TFL in a conjoint (5), chimeric (5) and multiple (3) free flaps manner. Most common perforator location was septo-cutaneous between the TFL and Gluteus Medius. There was complete flap loss in two cases and partial necrosis in two. No adjuvant therapy was delayed. Conclusion: TFLP can be used to counter ALT/AMT unavailability, injury, suboptimal quality or need of a thicker flap. Chimeric ALT-TFL can be harvested for large, complex, multicomponent and multidimensional defects. We recommend, harvesting flaps from the thigh with a non-committal straight line incision initially, perceiving ALT-AMT-TFL perforators as a unit.

Learning-based double layer control method of yaw stability simulation research for rear wheel independent drive electric tractor plowing operation

Complex field environments and variable soil conditions make tractor plowing operations susceptible to maneuvering instability, especially challenging in yaw stability. A learning-based double layer control (LDLC) method of yaw stability for rear wheel independent drive electric tractor (ET) plowing operation is proposed in this paper in order to solve this problem. Firstly, a sliding window self-learning traction resistance predictor is proposed based on Gaussian process regression (GPR) theory to predict the future traction resistance of plowing operation. Then, a discrete nonlinear model predictive control (NMPC) supervisor yaw stability controller is designed based on the dynamics model of the plowing unit and the tire-soil model to solve for the additional yaw torque required to maintain the yaw stability of the tractor. Finally, considering the additional yaw moment and driver demand torque, the subordinate controller composed of a particle swarm optimization algorithm optimally allocates the driving torque of the two driving wheels. Hardware-in-the-loop test results show that the maximum mean tracking errors of yaw rate and sideslip angle are 0.002 rad/s and 0.01 rad for the LDLC controlled ET during straight line and continuous steering under normal plowing operation, the maximum mean tracking errors of yaw rate and sideslip angle are 0.007 rad/s and 0.012 rad for straight line and continuous steering plowing operations under harsh plowing operation. The tracking accuracy is significantly higher than traditional cascade PID and equal distribution control methods. The proposed LDLC method effectively ensures the yaw stability of the ET during straight line and continuous steering under normal and harsh plowing operation conditions.

Study on the correlation of supplementation with L-citrulline on the gastrointestinal flora and semen antifreeze performance of ram.

Cryopreservation of semen can give full play to the reproductive advantages of male animals. However, in actual production, due to the poor frost resistance of sheep semen and the low conception rate, the promotion of sheep frozen semen is greatly hindered. Therefore, it is urgent to improve the frost resistance of semen to improve the quality of frozen semen. At present, most studies on improving the quality of frozen semen are based on the improvement of semen dilutions, and few studies on improving the freezing resistance of ram semen by feeding functional amino acids. Therefore, 24 Turpan black rams were divided into high antifreeze group (HF) and a low antifreeze group (LF) Each of these groups was further randomly divided into control and experimental subgroups. The control subgroup was fed a basal diet, while the experimental subgroup received an additional 12 g/d of L-Cit supplementation based on the control group for a duration of 90 days. The results showed that Following L-Cit supplementation, the experimental group demonstrated significantly elevated sperm density and VSL (Velocity of straight line), T-AOC, GSH-Px, and NO levels in fresh semen compared to the control group (P < 0.01). After thawing, the experimental group exhibited significantly higher levels of T-AOC, GSH-Px, and NO compared to the control group (P < 0.01). Additionally, the HFT group, after thawing frozen semen, displayed significantly higher HK1 protein expression compared to the control group. The number of spermatogonia, spermatocytes, and sperm cells in the HFT group was significantly higher than that in the HFC group. Moreover, 16S rRNA sequence analysis showed that Candidatus_Saccharimonas, Staphylococcus, Weissella, succinivbrionaceae_UcG_002, and Quinella were significantly enriched in the rumen of the HFT group, while Ureaplasma was significantly enriched in the HFC group. In the duodenum, Clostridiales_bacterium_Firm_14, Butyrivibrio, and Prevotellaceae_NK3831_group were significantly enriched in the HFT group, whereas Desulfovibrio and Quinella were significantly enriched in the HFC group. Under the conditions employed in this study, L-Cit supplementation was found to enhance the intestinal flora composition in rams, thereby improving semen quality, enhancing the antifreeze performance of semen, and promoting the development of testicular spermatogenic cells.

A ray-inspired flexible robot fish with stable controllability actuated by photo -responsive composite hydrogels with poly(N-isopropylacrylamide) and multi-walled carbon nanotubes

Drawing inspiration from the movement behaviour of rays in nature, we have successfully developed a ray-inspired flexible robot fish driven by visible light. A composite made of poly(N-isopropylacrylamide) (PNIPAM) and multi-walled carbon nanotubes (MWCNTs) has excellent biocompatibility and photo-responsive deformability. The PNIPAM hydrogel flexible material of the robot fish was prepared by light curing printing technology. Under the control of visible light, the robot fish swims in a straight line at an average speed of about 0.42 mm/s. The photoinduced asymmetric deformation mechanism is used to control the deformation of the fins on both sides of the robot fish, so that the robot fish can turn and realize directional swimming control. These findings have important implications for the development of flexible bionic robots and provide valuable insights for the research of bionic robots driven by visible light.

Safety of mapping the motor networks in the spinal cord using penetrating microelectrodes in Yucatan minipigs.

The goal of this study was to assess the safety of mapping spinal cord locomotor networks using penetrating stimulation microelectrodes in Yucatan minipigs (YMPs) as a clinically translational animal model. Eleven YMPs were trained to walk up and down a straight line. Motion capture was performed, and electromyographic (EMG) activity of hindlimb muscles was recorded during overground walking. The YMPs underwent a laminectomy and durotomy to expose the lumbar spinal cord. Using an ultrasound-guided stereotaxic frame, microelectrodes were inserted into the spinal cord in 8 animals. Pial cuts were made to prevent tissue dimpling before microelectrode insertion. Different locations within the lumbar enlargement were electrically stimulated to map the locomotor networks. The remaining 3 YMPs served as sham controls, receiving the laminectomy, durotomy, and pial cuts but not microelectrode insertion. The Porcine Thoracic Injury Behavioral Scale (PTIBS) and hindlimb reflex assessment results were recorded for 4 weeks postoperatively. Overground gait kinematics and hindlimb EMG activity were recorded again at weeks 3 and 4 postoperatively and compared with preoperative measures. The animals were euthanized at the end of week 4, and the lumbar spinal cords were extracted and preserved for immunohistochemical analysis. All YMPs showed transient deficits in hindlimb function postoperatively. Except for 1 YMP in the experimental group, all animals regained normal ambulation and balance (PTIBS score 10) at the end of weeks 3 and 4. One animal in the experimental group showed gait and balance deficits by week 4 (PTIBS score 4). This animal was excluded from the kinematics and EMG analyses. Overground gait kinematic measures and EMG activity showed no significant (p > 0.05) differences between preoperative and postoperative values, and between the experimental and sham groups. Less than 5% of electrode tracks were visible in the tissue analysis of the animals in the experimental group. There was no statistically significant difference in damage caused by pial cuts between the experimental and sham groups. Tissue damage due to the pial cuts was more frequently observed in immunohistochemical analyses than microelectrode tracks. These findings suggest that mapping spinal locomotor networks in porcine models can be performed safely, without lasting damage to the spinal cord.