Track Length Research Articles

Idle shake vibration optimization of an engine mounting system through the practical application of transfer path analysis

This article presents a practical application of experimental transfer path analysis (TPA) for optimizing idle shake vibrations of a front-wheel-drive car with a transversely mounted four-cylinder diesel engine. Performance control of the vehicle engine mounting system must take into account the multiple dynamic interactions between the engine mounting system, subframe modes and the vehicle suspension. Experimental methods can be used in conjunction with simulations to design and optimize the engine mounting system. TPA is a powerful tool for the diagnosis of vibration and noise transmission via multiple solid paths. TPA allows a quick diagnosis of the engine mounting system performances on vehicle comfort. A strong synergy between numerical model and experimental data finally makes it possible to find better design alternatives, not necessarily obvious to the designer. This study is the guideline for an optimization of the engine mount noise vibration and harshness (NVH) performances by using a hybrid approach, combining an analytical approach and measurement data. First, a diagnosis of the transmission of structure-borne vibrations via the engine mounting system to the seat floor is done at constant idle speed. This method is used to rank individual engine mount contributions in the low-frequency vibration level inside the vehicle. Then, an original approach allows the optimization of the vibration level at idle speed by offsetting contributions of the engine mount paths by adding damping in the right engine mount. This approach has led to the design and validation of an original double inertia-track hydroelastic mount prototype which allows a 5-dB reduction on the seat floor vibration level. The future development of a new version is planned to confirm and optimized the obtained results. The length of the second inertia track will be increased to reach the targeted characteristics, and the adjustment system will be removed to respect the overall dimension constraints of the mount.

Track circuits adjusting calculation method under current influence traction interference and electromagnetic compatibility

The problem of railway transport electromagnetic compatibility automation systems in recent years has been aggravated by the use of power frequency converters in electric transport drives, which significantly increase the efficiency of traction characteristics of 3-phase electric engine. However, estimate relevant harmonic levels in the frequency range used in track circuits of railway automation and telemechanic systems. The paper provides theoretical justification for practical measurements of interference. It is shown, that the interference coefficients monotonically increase in the following cases: 1) increase in the value of the harmonic frequency; 2) increase in the propagation constant, taking into account the supports resistance of the contact network; 3) increase in the circuits track length. Operating frequencies of tonal track circuits up to 800 Hz, the interference increase rate in given length of the rail circuit slows down. The increase in interference coefficients depending on the mentioned factors is explained by the fact that with current part growth of the harmonic flows from the traction substation through the earth increases and thereby creates currents asymmetry of the track circuits.

Evaluation of Radiation Shielding Features of Co and Ni-Based Superalloys Using MCNP-5 Code: Potential Use in Nuclear Safety

Due to their excellent heat resistance, superalloys are used predominantly in the manufacturing of engine parts and accessories for aircraft and aerospace equipment. The Monte Carlo simulation (MCNP-5) code was performed to estimate the mean track length of the incident photons inside six different alloys. Then, based on the simulated track length, other important γ-ray shielding parameters were calculated. In this study, the highest mass attenuation coefficient was obtained for alloys encoded MAR-302 and MAR-247 and varied in the range 0.035–72.94 and 0.035–71.98 cm2·g−1, respectively. The lowest mass attenuation coefficient was found for alloys coded Inconel-718 and Nimocast-75 with a range of 0.033–59.25 and 0.32–59.30 cm2·g−1, respectively. Use was made of a recently developed online program Phy-X/PD to calculate the effective atomic number, equivalent atomic number, and the buildup factors for the alloys of interest. The effective removal cross-section for the fast neutron was also calculated for the studied alloys: the highest value was found for the alloys coded with Inconel-718 (∑R = 0.01945 cm2·g−1) and Nimocast-75 (∑R = 0.01940 cm2·g−1), and the lowest value was obtained for alloy coded MAR-302 (∑R = 0.01841 cm2·g−1). Calculated data indicate that MAR-302 and MAR-247 are superior candidates for shielding of gamma-rays, while Inconel-718 and Nimocast-75 MAR-302 are suitable for the shielding of fast neutrons.

On the seasonal and sub‐seasonal factors influencing East China tropical cyclone landfall

AbstractTo date it has proved difficult to make seasonal forecasts of tropical cyclones, particularly for landfall and in East China specifically. This study examines sources of predictability for the number of landfalling typhoons in East China on seasonal (June–October) and sub‐seasonal time scales. East China landfall count is shown to be independent of basin‐scale properties of TC tracks, such the genesis location, duration, basin track direction and length, and basin total count. Large‐scale environmental climate indices which are potential basin scale drivers are also shown to be largely uncorrelated with landfall prior to and throughout the season. The most important factor is the steering in the final stages to landfall. The seasonal landfall is strongly anti‐correlated with the more local zonal mid‐tropospheric wind field over the East China sea (r = −.61, p < .001). It is proposed that geopotential height anomalies over Korea/Japan cause anomalous easterly winds in the East China Sea and enhance landfall rates by steering typhoons onto the coast. Early, peak, and late sub‐seasonal landfall counts are shown to be independent of each other yet share this predictor. This local feature may be dynamically predictable allowing a potential hybrid dynamical‐statistical seasonal forecast of landfall.

Assessment of internal organ stub injury frequencies and their infliction causes

Aim.Determination of most frequently cut-wounded internal organs and injury infliction causes.Material and methods.The article reports the results of a retrospective statistical assay of forensic medical reports of corpse examination conducted at the Khabarovsk Inter-District Forensic Examination Department of the Bureau of Forensic Medical Expertise, Ministry of Health of the Khabarovsk Region, in the years 20142018.Results.The study identified the frequency of sharp force injuries, the most frequently wounded internal organs and the average lengths of wound tracks in the entire body and particular internal organs.

Quantifying effects of tracking data bias on species distribution models

Abstract Telemetry datasets are becoming increasingly large and covering a wider range of species using different technologies (GPS, Argos, light‐based geolocation). Together, such datasets hold tremendous potential to understand species' space use at broad spatial scale, through the development of species distribution or habitat suitability models (SDMs) to predict environmental dependencies of species across space and time. However, tracking datasets can be heavily biased and an assessment of how such biases affect SDM predictions, and therefore, our interpretation of animal distributions is lacking. We generated simulated tracks based on predetermined environmental values for a random predator and a central place forager, and then sampled positions from those tracks based on a combination of five common biases in tracking datasets: (a) tagging location; (b) tracking device; (c) data gaps within tracks; (d) premature tag detachment (or failure) and (e) different processing methods. We then used 240 combinations of the resulting biased simulated datasets to develop binomial generalised linear (GLM) and additive (GAM) models to estimate habitat suitability in different environmental sets (cool deep, cool coastal, warm deep and warm coastal environments). Our results show that tagging location and length of tracks have the largest effects in decreasing model performance, but that these biases can be overcome by adding a small percentage of additional, relatively less biased tracks to the dataset. In comparison, the effects from all other biases were almost negligible, including for low resolution tracking datasets for which sufficient tracks are available. We also highlight the need for a cautionary approach when using processing methods that can introduce other biases (e.g. interpolated locations). Similar trends were obtained for the random predator and the central place forager, but with relatively lower model performance for the latter. We provide evidence that even non‐GPS tracking datasets can be readily used to improve the knowledge of large‐scale space use by species without the need for detailed processing and tracking reconstruction. This is especially relevant in the current context of rapid increase in data acquisition and the urgent need to address the large spatial scale ecological consequences of global change.

Why individuals choose dockless bike sharing services?

This study investigates dockless bike sharing service (DBS) users’ behavior; particularly, why individuals choose DBS. A latent segmentation-based logit (LSL) model is developed using data from a DBS user survey conducted in Kelowna, Canada. The model is developed considering the following reasons for choosing DBS: cheapest option, fastest option, exercise purposes, recreational purposes, parking constraint, and unavailability of other modes or other reasons. The LSL model captures unobserved heterogeneity by assigning individuals into discrete latent segments. The model is estimated for two segments. Results suggest that segment 1 can be identified to include older, lower-income, frequent bike rider, females; whereas, segment 2 includes higher income, younger, non-frequent bike user, males. The parameter estimation results suggest that built environment attributes such as bike index, land use diversity index, transit accessibility, density of destinations, and length of bike infrastructure might influence the choice of DBS. The model confirms significant heterogeneity across the segments. Individuals residing in mixed land use areas with longer active transportation infrastructure are more likely to use DBS for recreational purposes in segment 1. In contrast, higher-income individuals in segment 2 show a negative relationship. The elasticity effects suggest that transit accessibility, length of bike lanes and cycle tracks, dwelling density, and vehicle ownership reveal substantial impact in segment 1. In contrast, bike index, land use diversity index, and personal vehicle ownership reveal significant impact in segment 2. This study offers important behavioral insights; specifically, the heterogeneity addressed in this research needs to be accommodated within the policy-making for efficient operation and expansion of DBS.

A quantitative description of fission-track etching in apatite

Abstract We measured the apatite etch rate νR in 5.5 M HNO3 at 21 °C as a function of orientation. Results for Durango apatite evidence that νR varies by a factor >5 with angle to the c-axis. Our measurements also provided track etch rates νT and surface etch rates νS. However, these cannot be combined for calculating track etching or counting efficiencies. By inserting the measured etch rates in a recent model, we calculate the geometries and dimensions of surface tracks in different apatite faces. The proposed model must be recalibrated for different etching protocols and adapted for other minerals. We submit that the new model justifies reviewing track counting efficiencies based on the existing (νB-νT) etch model. We anticipate that this will have an effect on practical aspects of fission track dating. Single-track step-etch data show that the confined track lengths increase with etch time at a decreasing average rate νL that differs from the track etch rate νT and the apatite etch rate νR. Both νT and νL exhibit large track-to-track differences that produce irreducible length variation related to the latent-track structure resulting from formation and annealing. Step etching and track width measurements are effective for reducing or eliminating procedure-related artifacts from track length data, and so for accessing more fundamental track properties.

THE EFFECT OF GOLD NANOPARTICLES ON RADIATION DOSE DISTRIBUTION IN BREAST CANCER USING MONTE CARLO SIMULATION

The simulation model for MCNP5 code was used to study the effect of the gold nanoparticle (AuNPs) in cancer breast samples. The dose rate distribution of AuNPs in water and breast phantom was calculated using MCNP5 code. For inhomogeneities, cone cells were designed to calculate dose distribution around Ir-192 source in breast and inhomogeneous medium that includes gold nanoparticles at different concentration. Both barometers, the track length energy deposition tally (F6) and pulse height tally (*F8), were used. The result indicated that the F6 is better than *F8 for radiation dose calculation. Angular doses distribution in water was compared with data published for tally F6 and*F8 with the different percentage range of 0.0136 to 0.3019% for tally F6 at the average angle of 5˚and 175˚respectively. For *F8 tally, different percentage range of - 0.0014 to 0.8253 % was obtained at an average angle of 75˚and 5˚ respectively. For breast phantom, the result of the F6 tally with the *F8 tally was compared. The difference in calculations between the two tallies in the angular anisotropic distribution was found to be in the range from 0.0514 to 0.4596% at the average angle of 15 ˚ and 175 ˚ respectively. The obtained results showed that the AuNP dose increases when the concentration increases up to ten percent (100 mg/ml), and then decreases for concentration higher than ten percent. The concentration of AuNPs greater than ten percent is not recommended. The results indicated that tally F6 is a good tool to calculate the effect of inhomogeneities due to breast cancer on brachytherapy.

Apatite Fission Track Signatures of the Ross Sea Ice Flows During the Last Glacial Maximum

AbstractThe catchment for the Ross Sea ice includes both the East and the West Antarctic ice sheets, but the mass balance is a direct response to climate change. Our work is aimed to reconstruct the ice flows after the Last Glacial Maximum and is based on apatite fission track data from samples collected from 18 piston cores across the Ross Sea embayment. Fission track ages have been divided into meaningful populations and then compared with bedrock ages from West and East Antarctica. Furthermore, fission track lengths have been measured on each population and then compared through forward modeling with thermal histories derived from literature. The widespread presence of apatites with cooling ages of about 30–40 Ma reveals a main exhumation phase of the Transantarctic Mountains during the Oligocene associated to the last phases of the West Antarctic Rift System. Furthermore, the presence of key marker apatites (e.g., younger than 21 Ma or older than 230 Ma) allows to identify the Central High as a major ice flow divide.

Modelling track and ground vibrations for a slab ballastless track as an infinitely long periodic structure subject to a moving harmonic load

This paper presents a model for predicting ground vibration generated from a slab ballastless track, subject to a moving harmonic load. The track consists of four layers: two rails, track slabs, bed plates and a track base resting on the ground. Different from existing models for slab tracks, the one developed in this paper takes into account both the discrete supports to the rail and the discontinuity of the slabs and bed plates, and treats the track/ground system as an infinitely long periodic structure. The rail and the base are represented as, respectively, an infinitely long Timoshenko beam and an infinitely long Euler-Bernoulli beam. The slabs and bed plates are modelled as Euler-Bernoulli beams of finite length, of which the responses are formulated using the mode superposition method. By using square window functions, the differential equations of motion of each track slab and bed plate are defined for the entire track length. The ground is idealised to be a horizontally layered structure. The steady-state response of the track/ground system is sought and formulated in the frequency-wavenumber domain. By using the periodic condition of a periodic structure, it is shown that the steady-state response of the track/ground system can be determined by the modal coefficients of the slabs and plates in the 0th unit cell (the 0th bay). Formulae are derived for these modal coefficients. Results including receptances of the rail, displacement spectra of the ground and critical speeds of an axle load are produced for two sets of track/ground parameters and compared with those when the slab and bed plates are assumed to be continuous beams, demonstrating when the later treatment works. The role of veering in dispersion curves of a periodic track in critical speed is identified. Formulations in this paper can be directly applied to the Chinese CRTS II and III tracks on a layered ground. They provide a basis for developing a complete ground vibration prediction model that incorporates a moving train, an infinitely long periodic track and a homogeneous or horizontally layered ground. They can also be used to assess if a periodic track/ground system can be simplified to be invariant in the track direction.

Railway Planning Double-Double Track (Case Study of Bekasi Station km 26 + 652 - Jatinegara Station km 12 + 050

Increasing the number of population and the development of activities will cause a growing need for space every day, this will result in physical changes and urban land use and can cause increased intensity of population movement from Megapolitan cities such as Bekasi, Bogor and Tangerang to the Metropolitan city (DKI Jakarta). Some people have now started to move from private vehicles to use public (mass) transportation such as buses, transjakarta, and electric rail trains or commonly known as KRL Commuter Line that serve Jabodetabek routes. The impact of crossing also causes buildup at each station. Train track with a single track (single track) is considered ineffective and inefficient and vulnerable to train accidents due to human error. It is necessary to develop or develop a double track to become a double-double track Bekasi Station km 26 + 652 - Jatinegara Station km 12 + 050. The research location is on the railway line from Bekasi Station to Jatinegara Station. The length of the train track is around 16 km and has 7 stations that are traversed, 5 of which are active (stop) and 2 passive stations.

Evaluation of track length, residence time and translational speed for tropical cyclones in the North Indian ocean

ABSTRACT The present study performed a critical examination on the historical tracks of 185 tropical cyclonic events that developed over North Indian Ocean basin during the past 37 years (1982–2018). Analysis of cyclone tracks was carried out including all categories starting from Deep Depression (DD) to Super Cyclonic Storm (SuCS) stages. Results from the study indicate that the track length have decreased by about 13%, whereas the residence time increased by 7.3% for all categories considered during the study period. However, the high-intense cyclone categories showed an increase in both track lengths and residence time that was statistically significant. The net increase was about 10% and 43% for the track lengths and residence time, respectively. Segmented analysis clearly brings out the significant upward trend in track length and residence time during the recent decade (2009–2018). Further, the study examined the variability in translational speed on annual and inter-seasonal scales for cyclonic disturbances that formed over the Bay of Bengal basin. The overall trend is showing a decreasing pattern with a net reduction of 2.5 km/h over the past three decades. A detailed assessment was carried out to understand the trends in these parameters for the North Indian Ocean region. The study has practical implications in better understanding the characteristics of tropical cyclones and coastal vulnerability.

Preliminary observation of the migration of sodium fluorescein along meridians in the limbs of mini-pigs

<p indent=0mm>Meridians are a core concept in traditional Chinese medicine (TCM) theory. It has been shown in many previous studies that meridians exist in the interstitium, the space through which interstitial fluids flow. Sodium fluorescein (SF) is a small, fluorescent, hydrophilic molecule. SF was injected into the low impedance points (LIPs) or the high impedance points (HIPs) on the limbs of healthy mini-pigs, as determined by a low impedance meridian locator (WQ6F30). Migration tracks were scanned by a digital camera (Canon 5D2) with a narrow band filter and colored flash lamps prior to and after SF injection. The relationships between superficial veins and SF tracks were analyzed using a projection vein finder (V800P). Tissues were frozen on dry ice, and the distribution of SF in the transverse sections of SF tracks was observed. Results reliably showed that seven migrating tracks along the low impedance line along meridians (LILM) were found when SF was injected at LIPs, three of which were on the outside of forelimb, three of which were on the inside of forelimb, and one of which was on the inside of hind limb. The average length of these migration tracks was <sc>5.13 cm.</sc> The migration tracks were 81.4% consistent with LILM, while no overlap was observed with veins. The shape of injected SF in the transverse sections was similar to an inverted triangle, and distributed in the muscle gap. No linear migration was observed when SF was injected at HIP, and the shapes of injected SF were nearly round by local diffusion. The length, width and length-width ratio of SF shapes between injections at LIPs and HIPs were significantly different (<italic>P</italic><0.01). These results imply that the concept of the meridian in TCM may be an unknown interstitial channel.

Modeling Destination Choice Behavior of the Dockless Bike Sharing Service Users

This study investigates trip-level destination choice behavior of users of the dockless bike sharing service (DBS). A random parameter latent segmentation-based logit (RPLSL) model is developed utilizing the DBS users’ trip itinerary data for Kelowna, Canada. The RPLSL model captures multi-dimensional heterogeneity such as inter-segment and intra-segment heterogeneity. The model is developed at a micro-spatial resolution which is defined as the bicycle analysis zone. One of the key features of this study is to test the interdependencies between the origin and destination of a trip using their built environment attributes. Model results suggest that segment 1 is more likely to include trips originating from the urban neighborhoods; whereas, segment 2 includes trips originating from the suburban neighborhoods. The parameter estimation results reveal that DBS trips are more likely to be destined to locations with longer length of cycle tracks, higher employment density, and that are closer to the Central Business District and bus stops (i.e., within 500 m). The model confirms multi-layer heterogeneity. For instance, trips originating from the urban areas in segment 1 are more likely to be destined to destinations within 500 m of the designated bike return sites (i.e., havens). In contrast, shorter trips originating in suburban areas in segment 2 show a negative relationship. Interestingly, a bike-friendly environment might increase the attractiveness of destinations closer to havens, even for the trips originating in suburban areas. The findings of this study will assist in developing policies and infrastructure investment decision making at the destination locations to promote DBS usage.

Seamless low-temperature thermochronological modeling in Andino 3D, towards integrated structural and thermal simulations

We present the development of thermochronological tools for Andino 3D® software, that integrates Fetkin (Finite Element Temperature Kinematics). These tools allow the user to work on both the structural and the thermochronological model at the same time, providing a user-friendly environment that overcomes the need to work with different programs. Thermochronological and structural models can be checked and eventually corrected in a visual and intuitive form by following a 4-step workflow. The first step of such workflow is to define the thermochronological computing grid, checking in real time, if the resolution and coverage are satisfactory. After that, the interpolation process can be done, whereby velocity vectors for all nodes in beds and faults are calculated for all interpolated times. The third step of the workflow consists of filling thermal properties and velocities for all grid cells. The final step is the calculation of the thermal state at each time in the reconstruction. Boundary conditions (basal temperature, basal heat flow, surface temperature and altitude gradient) are defined by mouse picking as constant, spatially varying, time varying or spatially and time varying. To check the feasibility of a structural model, thermochronological samples can be defined at desired positions to predict time-temperature variations. Simulated fission track ages, mean track lengths and age standard deviations can be calculated for different minerals (apatite and zircons). Also, cooling ages and %Ro can be simulated for (U–Th-Sm)/He and vitrinite systems, respectively. The Carohuaicho structure in the southern Bolivia sub-Andean Ranges is presented as a case of study to demonstrate these tools. Andino 3D® allowed us to successfully simulate the t-T paths of four samples where (U–Th-Sm)/He measurements were available. The different models performed permitted us to conclude that a low geothermal gradient was likely to be present during the last 7 Ma of Andean deformation in the study region.

Representative Sample Sampling Method for Size Effect Experiment of Jointed Rock Mass

The influence of size effect on the hydromechanical behavior of rock mass has long been recognized. As a result, analysis of the rock mass size effect has been developed. However, when conducting size effect studies, the representativeness of the sample is less considered. Therefore, combining the existing statistical methods and sampling methods, a comprehensive representative sampling method for rock mass is present. In this method, a large number of sample statistics of different sizes are provided in the progressive coverage method; then, the plane density of the track length is defined as the value of stratification to perform stratified sampling for representative samples. Furthermore, it is applied to a joint network model generated in accordance with the actual situation and compared with those of other methods. The sampling results show that the proposed method can provide a certain reference value for studying the scale-dependent behavior of rock mass mechanical parameters.

Object-based tracking of precipitation systems in western Canada: the importance of temporal resolution of source data

Object-based algorithm provides additional spatiotemporal information of precipitation, besides traditional aspects such as amount and intensity. Using the Method for Object-based Diagnostic Evaluation with Time Dimension (MODE-TD, or MTD), precipitation features in western Canada have been analyzed comprehensively based on the Canadian Precipitation Analysis, North American Regional Reanalysis, Multi-Source Weighted-Ensemble Precipitation, and a convection-permitting climate model. We found light precipitation occurs frequently in the interior valleys of western Canada while moderate to heavy precipitation is rare there. The size of maritime precipitation system near the coast is similar to the continental precipitation system on the Prairies for moderate to heavy precipitation while light precipitation on the Prairies is larger in size than that occurs near the coast. For temporal features, moderate to heavy precipitation lasts longer than light precipitation over the Pacific coast, and precipitation systems on the Prairies generally move faster than the coastal precipitation. For annual cycle, the west coast has more precipitation events in cold seasons while more precipitation events are identified in warm seasons on the Prairies due to vigorous convection activities. Using two control experiments, the way how the spatiotemporal resolution of source data influences the MTD results has been examined. Overall, the spatial resolution of source data has little influence on MTD results. However, MTD driven by dataset with coarse temporal resolution tend to identify precipitation systems with relatively large size and slow propagation speed. This kind of precipitation systems normally have short track length and relatively long lifetime. For a typical precipitation system (0.7 $$\sim $$ 2 $$\times $$ 10 $$^{4}$$ km $$^{2}$$ in size) in western Canada, the maximum propagation speed that can be identified by 6-h data is approximately 25 km h $$^{-1}$$ , 33 km h $$^{-1}$$ for 3-h, and 100 km h $$^{-1}$$ for hourly dataset. Since the propagation speed of precipitation systems in North America is basically between 0 and 80 km h $$^{-1}$$ , we argue that precipitation features can be identified properly by MTD only when dataset with hourly or higher temporal resolution is used.

Track length measurement of [formula omitted] ions with the MIMAC directional Dark Matter detector prototype

Weakly Interacting Massive Particles (WIMPs) are one of the most preferred candidates for Dark Matter. WIMPs should interact with the nuclei of detectors. If a robust signal is eventually observed in direct detection experiments, the best signature to confirm its Galactic origin would be the angular distribution of nuclear recoil tracks (Spergel, 1988). The MIMAC collaboration has developed a low pressure gas detector providing both the kinetic energy and three-dimensional track reconstruction of nuclear recoils. In this paper we report the first ever observations of 19F nuclei tracks in a 5 cm drift prototype MIMAC detector, in the low kinetic energy range (6–26 keV), using specially developed ion beam facilities. We have measured the recoil track lengths and found significant differences between our measurements and standard simulations. In order to understand these differences, we have performed a series of complementary experiments and simulations to study the impact of the diffusion and overall systematics. We show an unexpected dependence of the number of digitizer time bins corresponding to the track on the electric field applied to the 512µm gap of the Micromegas detector. We have introduced, based on the flash-ADC observable, corrections in order to reconstruct the physical 3D track length of the primary electron clouds before avalanches, proposing the physics behind these corrections. We show that diffusion and space charge effects need to be taken into account to explain the differences between measurements and standard simulations. These measurements and simulations may shed a new light on the high-gain TPC ionization signals in general and particularly at low energy.

Molière maximum likelihood proton path estimation approximated by cubic Bézier curve for scatter corrected proton CT reconstruction

A maximum likelihood approach to the problem of calculating the proton paths inside the scanned object in proton computed tomography is presented. Molière theory is used for the first time to derive a physical model that describes proton multiple Coulomb scattering, avoiding the need for the Gaussian approximation currently used. To enable this, the proposed method approximates proton paths with cubic Bézier curves and subsequently maximizes the path likelihood through parametric optimization, based on the Molière model. Results from the Highland formula-based Gaussian approximation are also presented for comparison. The simplex method is utilized for optimisation. The scattering properties of the material(s) of the scanned object are taken into account by appropriately calculating the scattering parameters from the stopping power map that is calculated/updated at every iteration of the algebraic reconstruction process. Proton track length constraint imposed by the proton energy loss is accounted for. The method is also applied in the case that no exit angle data are measured. Geant4 Monte Carlo simulations were performed for model validation. Our results show that use of Molière probability density function for modelling the multiple Coulomb scattering presents a modest 2% accuracy improvement over the Gaussian approximation and most-likely-path method. Simulations of voxelized phantom showed no essential benefit from the inclusion of the material information into the optimization, while path optimization with energy constraint slightly increased path resolution in a bone/water interface phantom. Method error was found to depend on energy, proton track-length within the medium, and proportion of data filtering.