Elementary Segments Research Articles

3-D Current Density and Magnetic Field of 3-D MR Scanner Gradient Coil

The topic of this paper is to describe the 3-D current density in the windings of a 3-D coil, which fills the volume between two coaxial cylinders at a precisely defined distance from each other, and which serves to generate a magnetic field gradient in the center of the cylinder axis. The 3-D current density is considered an unknown input quantity, which is calculated from the known gradient magnetic field output. It is an inverse problem in mathematics, where the direct problems are the calculation of unknown output quantities based on known input quantities. Fourier series expansion methods in the context of cylindrical coordinates were used to describe the 3-D current density. In that case, Bessel functions are used as development components. The current densities, at each point in space, were lined up to represent current lines. Each power line is associated with a coil winding through which a current of a certain strength flows. After that, the principle of discretization of coil windings was applied. Each winding is divided into a large number of elementary segments that were considered as current elements, which create, based on Bio-Savar's law, an elementary magnetic field. In this way, the total, continuous magnetic field is broken into many elementary components, which come from different current elements. An important result of this process is that each current element can be controlled independently by a current source. This means that the output magnetic field of the gradient can be controlled by current sources, which are the input sizes, and this is what is at the core of the topic of this paper.

CUBIC B-SPLINES: PRACTICAL APPLICATION

Two constructive algorithms for forming cubic B-splines passing through given points with tangents indicated at these points are proposed. The first algorithm provides a composite cubic B-spline curve passing through n reference points. The composite curve is formed by 3(n-1) elementary cubic segments. At the reference points, the curvature of all segments is zero. Controlling the shape of the curve (with given tangents at the reference points) is achieved by moving auxiliary control points along the given tangents. The second algorithm allows the formation of a cubic B-spline that passes only through two predefined points, but with the ability to control the shape of the spline by moving arbitrarily specified control points. The cubic B-spline equations are derived using two, three, and four control points. For the case of “two control points,” a wellknown result is obtained: the equation of the B-spline identically coincides with the equation of the cubic Bezier curve. For the case of “three control points,” the B-spline equation consisting of two segments is obtained. For the case of “four control points,” we obtain the equation of a cubic curve consisting of three segments. The proposed algorithms enable users to practically construct cubic B-spline curves using the equations derived in the article. The resulting equations allow, without using the Coxde Boer recurrent formula, the calculation and construction of cubic B-splines with three or four control points, respectively. The article presents the basic theoretical information about cubic B-spline curves necessary to solve these problems. Practical examples of constructing composite cubic B-spline curves are provided. The tasks considered in the article can be solved in any graphics editor using NURBS curves, which have become a standard tool for computer modeling. However, this graphical tool does not provide a mathematical model of the curve in the form of equations. On the contrary, the algorithms considered in the article ensure the derivation of the equations of the constructed curves.

Optimal deployment of dynamic wireless charging facilities for electric bus route considering stochastic travel times

Installing dynamic wireless charging (DWC) facilities on dedicated bus lanes endows electric buses (EBs) with the ability to charge while in motion, effectively overcoming the limitations of short driving ranges. However, if the facilities are deployed along the entire EB route, it would incur significant economic costs and result in resource wastage. In this study, we divide the EB route into segments including station segments, intersection segments, and elementary segments of road section. The fluctuations in travel times of different trips on these segments are described. To optimize the DWC deployment plan, a chance constraint programming model is established with the objective of minimizing the costs of purchasing power transmitters and inverters. A combined algorithm using stochastic simulation and particle swarm optimization is designed to solve the model. A real EB route is used to conduct the case study, and results indicate that it is more suitable to deploy DWC facilities in adjacent elementary segments of road section compared to individually distributed station segments or intersection segments. Additionally, as wireless charging power or battery capacity increases, the number of required inverters and the length of power transmitters decrease, resulting in a nonlinear decrease in the deployment costs of charging facilities.

SEHATI (Screening and Health Education Holistic Integratif) Berbasis Multiple Intelligences Serta Young Health Leader Pada Siswa SDN Selorejo 1

SDN 1 Selorejo is still classified as a school with limited facilities. Educational support facilities include classrooms, libraries, UKS, school gardens and sanitation. The condition of educational support facilities seems to be poorly maintained, especially UKS, school gardens and sanitation due to the lack of human resources and school management related to school activities. Aspects of school and student activities and development are not well structured, activities are incidental and not sustainable. The post- pandemic new normality period is very important for implementing health holistically. The application of Multiple Intelligences allows students to explore new areas of intelligence and increase curiosity and natural talents by using the body, senses and imagination, and practice to understand promotive and preventive health concepts well. Elementary school age children will be trained to have leadership skills from an early age. This concept was developed in a holistic integrated manner due to various factors that can influence health levels in terms of host, agent and environment. The SEHATI program has 4 main activities, namely 1) Indoor Activity, 2) Health Screening (optimization of UKS), 3) Young Farmer (optimization of the environmental love program), and 4) Outdoor Activity. SEHATI activities involve the active contribution of partners to achieve goals. The SEHATI program is designed to prioritize behavior change efforts which include changing attitudes, habituating activities, and strengthening healthy behavior. With this health effort model, partners can implement health efforts well and sustainably and have awareness of the importance of implementing and understanding health efforts for children. In addition, schools can become role models for schools with effective health efforts in the elementary school segment in Indonesia

Fast and Accurate Transient Analysis of Thin-Wire Structure in Half-Space With PEEC Method

This article presents an efficient full-wave partial element equivalent circuit (PEEC) method of thin-wire structure in half-space for lightning transient analysis. In the framework of the PEEC formulation for thin-wire conductors, the partial elements are computed by double-folded line integrals. In layered media, the interaction integrals involve dyadic Green's functions, which contain a closed-form part and a Sommerfeld-integral part. The direct numerical computation of these integrals is very challenging and time-consuming, which hinders the practical application of the full-wave method. However, the efficient and accurate evaluation of partial elements has not been investigated in a comprehensive way so far. Accordingly, this article presents an efficient method for the evaluation of the partial elements between elementary segments in half space. The main novelty is that the interaction integrals are computed through a combination of the Taylor series expansion of the full-wave free space Green's function and the Sommerfeld-integral adaptive interpolation technique, which significantly reduces the computation time. The new method is systematically validated on examples from finite-difference time-domain (FDTD) method and method of moments and experimental results. The proposed method is validated with the NEC code in the frequency domain and the FDTD in the time domain.

Motivation of teachers of Rio de Janeiro state public network

In 2011, the Government of the State of Rio de Janeiro, through the State Department of Education, presented an Education Program to improve quality indices in the elementary and high school segments. In this context, it is necessary to verify if the educational program tends to motivate the teachers of the respective education network and, in this aspect, the present article aims to identify the factors related to motivation, perceived by the teachers in relation to the program established herein, according to the motivational theory of the two factors, by Frederick Herzberg, whose path includes describing the aforementioned motivational theory, knowing the State Education Program, its origin and objectives, and establishing a statistical framework on the motivation of teachers in a given space and time. Based on a quantitative-qualitative study, interviews were carried out through semi-structured questionnaires, aimed at teachers working in the neighborhoods of Campo Grande and Santa Cruz, metropolitan region of Rio de Janeiro, whose results evidenced the perception of the interviewed teachers regarding the motivational factors or intrinsic as well as hygienic or extrinsic factors.

Calculation of the force and kinematic parameters of the transfer mechanism based on a twisted arm chain

Introduction. The paper presents a brief kinematic analysis, as well as the application of D'Alembert's principle to finding the relationship between the force parameters in the transmission mechanism of a robotic manipulator constructed from a twisted arm chain. The use of this transfer mechanism can enhance the life of the arm actuator, the accuracy of its positioning, and increase the workload compared to the flexible linkage actuators (twisted strings). The work aimed at obtaining dependences between the displacements of circuit elements, as well as their force parameters required to monitor the control system operation of these devices.Materials and Methods. In the course of solving the problem, an elementary segment (element) of the transmission chain was considered. To find the relationship between the loads in the element, the virtual displacement principle was used. When finding kinematic connections between displacements, a brief geometric analysis of the transmission chain element was carried out. To conduct a comparative analysis of the analytical dependences obtained, a simulation technique implemented on a graphical link model using the NX software package was applied.Results. In the course of the study, we obtained dependences for determining the magnitude of the moment developed on the input link, depending on the external workload and its rotation angle, as well as for defining the linear displacement of the output link. A simulation model of the actuator was constructed, which can be applied in the dynamic study of the actuator mechanism, taking into account the inertia of the links.Discussion and Conclusions. From the obtained analytical dependences, we determined the value of the angle of rotation of the input link of the mechanism element, at which the maximum torque value for a fixed workload on the output element was achieved, as well as the maximum linear displacement of the output link. The calculated values were in good agreement with similar values obtained from the results of the simulation experiment, which gave us the possibility of using analytical dependences in the formation of a robot control system. In addition, these dependences made it possible to provide the selection of actuators with the required force indicators.

SCHEME OF MULTIPLICATIVE REPRESENTATIONS FOR A STOCHASTIC EQUATION WITH TWO WIENER PROCESSES

In this paper we consider a stochastic differential equation with two independent Wiener processes in an infinite-dimensional Hilbert space. This equation can be a mathematical model of a dynamic system in the presence of several independent perturbing random factors. To study the parameters of this equation, the Daletsky-Trotter method of multiplicative representations is used. This method is applied to both deterministic and stochastic equations. The method consists in the following: one constructs a partition of the interval of existence of the solution [t0, T] into elementary [tk+1, tk]. On each elementary segment, the evolutionary resolving operator of the complete equation S(tk+1, tk) is considered, as well as the product of the resolving operators of equations that are fragments of the complete equation =Q1k×S1k×S2k
 Thus, two multiplicative families consisting of different resolving operators are compared. When the equivalence conditions, which are verified in this paper, are satisfied, it can be argued that the solution of a stochastic equation can, in a certain sense, be represented as a composition of the corresponding solutions of differential equations on elementary intervals, the right parts of which are drift, and, accordingly, diffusion.
 Moreover, in order to implement such a multiplicative scheme in the case of several independent Wiener processes, additional requirements regarding diffusion coefficients should be imposed. Namely: the diffusion coefficients must be commuting operators, continuous in time.
 The scheme of multiplicative representations is based on the study of the parameters of evolutionary families of decision operators, as well as their estimates in the norms of the corresponding spaces. In this case, to obtain a certain estimate, several iteration steps are considered for the corresponding equations in the Hilbert space. It should be noted that the scheme of multiplicative representations can be interpreted as a scheme for obtaining an approximate solution.

Plasmonic origami: tuning optical properties by periodic folding of a gold nano film

Novel plasmonic structures are on the rise, with applications varying from sensing and spectroscopy to solar cells and biological therapies. In this work, we introduce a plasmonic metasurface with a very rich dispersion spectrum, measured both experimentally and numerically. It shows a tunable absorption that depends on the folding angle and periodicity. A detailed numerical analysis identifies the presence of quasi-omnidirectional absorption. This broad directional absorption mode matches a Fabry–Perot resonance of a surface plasmon polariton along an elementary segment of the periodic structure. This geometry induced wide directional absorption is highly promising for a variety of photonic, light harvesting, and sensing applications.

Elementary discourse unit segmentation for Vietnamese texts

Elementary discourse unit segmentation for Vietnamese texts

Consensus of Multi‐Agent Systems with Switching Disconnected Topologies via Elementary‐Unit‐Based Dwell Time Approach

In this study, a leader‐following consensus problem is investigated for a class of multi‐agent systems with switching disconnected topologies. Different from the existing results on switching disconnected topologies, the multi‐agent systems considered in this study are unstable. In this situation, the disconnected agents can disperse over some periods even if there exists control protocol on them. To break through this challenge, we draw lessons from which an appropriate switching law can stabilize the switching unstable systems and propose a novel approach called elementary‐unit‐based dwell time (EUBDT) approach. Based on this approach, each switching interval is considered to consist of a certain number of elementary time segments. Then, by analyzing the local variation of the error states within each elementary time segment, the stabilization properties of switching behaviors are derived to compensate the divergence within the switching intervals. Based on this, the sufficient conditions for the leader‐following consensus can be obtained by using a novel kind of piecewise time‐varying Lyapunov functions (PTVLFs). Moreover, a time‐scheduled controller is designed for such system. Finally, a numerical simulation is given to illustrate the theoretical approach.

Elementary discourse unit segmentation for Vietnamese texts

Elementary discourse unit segmentation for Vietnamese texts

Вибір складу, параметрів робочого процесу і режиму роботи силової установки літального апарата з надзвуковою крейсерською швидкістю польоту

The issues of choosing a composition, operating process parameters and operating modes of propulsion for supersonic cruising aircraft providing transoceanic flights are considered. A condition of maximum payload relative mass is used as a criterion for choosing the composition of the propulsion. This criterion can be transformed using the aircraft mass balance equation into a condition of the minimum relative mass of fuel and propulsion. A predictor-corrector method is used to solve the task. Choosing the composition, operating process parameters and operating modes of propulsion according to the cruising segment, taking into account the remaining flight segments takeoff, climb and descent by the empirical coefficients, is used as a predictor stage. Based on the solving results of this stage, the best competing variants of propulsions are selected for the purpose of subsequent more detailed analysis at a corrector stage by numerically solving the differential equations of the aircraft motion along an entire flight profile. At the same time, on each elementary section of the path, the control parameters of the propulsion are optimized according to the criterion of the minimum required fuel consumption to overcome this section. Propulsion with turbojet engine, turbofan and mixed flows turbofan engine, turbo-ramjet engine and turbofan engines that have ramjet modes are considered. Patterns of the change in the relative mass of the fuel and propulsion for the indicated compositions of the propulsions according to cruising segment of the flight for the cruising speeds corresponding to the M = 1.5...4 are established. These dependencies make it possible to select variants of propulsion competing in terms of payload for a cruising speed or select the most advantageous cruising speed for propulsion composition which is given. These dependencies were used to determine competing variants of the power plant, providing a minimum of the relative mass of fuel and propulsion for the airplane with a cruising speed corresponding to the M = 3. At the stage of the corrector, these variants of the propulsion were evaluated according to the criterion of the relative mass of fuel and propulsion by solving the equations of the aircraft motion along the entire flight profile with the optimization of the control parameters of the propulsion on each elementary segment of the profile according to the criterion of minimum fuel consumption to overcome it. In doing so, the operating process parameters of the propulsion were optimized near of those values that were obtained at the stage of the predictor. The analysis of the obtained results indicates that, in comparison with the predictor stage at the corrector stage, the parameters of the propulsion operating process that are optimal from the point of view of the relative mass of fuel and propulsion changed by about 12.5 %, and the relative mass of fuel and propulsion by about 3...4 %.

MULTIPLICATIVE APPROXIMATION OF A RANDOM PROCESS

In this paper we consider the stochastic Ito differential equation in an infinite-dimensional real Hilbert space. Using the method of multiplicative representations of Daletsky - Trotter, its approximate solution is constructed.
 Under classical conditions on the coefficients, there is a single to the stochastic equivalence of solutions of the stochastic equation, which is a random process. This development generates an evolutionary family of resolving operators by the formula x(t)= S(t, Construct the division of the segment by the points. An equation with time-uniform coefficients is considered on each elementary segment . There is a single solution of this equation on the elementary segment, which generates the resolving operator by the formula The multiplicative expression is constructed. Using the method of Dalecki-Trotter multiplicative representations, it is proved that this multiplicative expression is stochastically equivalent to the representation generated by the solution of the original equation. This means that the specified multiplicative expression is respectively a representation of the solution of the original equation. That is, the probability of one coincides with the solution of the original stochastic equation. It should be noted that this is possible under additional conditions for the coefficients of the equation. These conditions are the time continuity of the coefficients of the equation. Thus, the constructed multiplicative representation can be interpreted as an approximate solution of the original equation. This method of multiplicative approximation makes it possible to simplify the study of the corresponding random process both at the elementary segment and as a whole.
 It is known, that the solution of a stochastic equation by a known formula generates a solution of the inverse Kolmogorov equation in the corresponding space. This scheme of multiplicative approximation can be transferred to the solution of the parabolic equation, which is the inverse Kolmogorov equation. Thus, the method of multiplicative approximation makes it possible to simplify the study of both stochastic equations and partial differential equations.

E-P Heritage Value Assessment Method Proposed Methodology for Assessing Heritage Value of Load-Bearing Structures

ABSTRACT Gathering knowledge and data for diagnosis is highly important for the safeguarding and conservation of architectural heritage. These data should be organised in order to create a complex list of procedures to find sufficiently sensitive, effective and reasonably inexpensive technical processes to survey and to repair, renew and maintain load-bearing structures of potential heritage values. 1 1 Evaluation per Partes or Evaluation by Parts method developed by Eberhardt and Pospisil for assessing sensitivity of heritage valuable buildings and structures to invasiveness of diagnostics and repair methods. The research is based on an analysis of the concept “heritage value” 2 2 Grant of the Ministry of Culture of the Czech Republic NAKI DG18P02OVV033. The NAKI program’s vision is to achieve the maintenance and sustainable development of a specific national and cultural identity and integrity and cultural heritage in the context of European and world culture in the 21st century and in the conditions of expected global change through applied research and development. (see: Program na podporu aplikovaneho vyzkumu a experimentalniho vyvoje narodni a kulturni identity na leta 2016 až 2022, NAKI II, p. 6, Ministry of Culture of the Czech Republic, Prague 2013). . As a typical multidisciplinary field of research, practical tasks in heritage preservation show that heritage value should be understood as a complex value composed of varied elementary segments coming from different fields of human activities. Whereas each field has its own logical verifying rules and its own research methodology, each elementary segment is evaluated separately. The present article introduces the “E-P Heritage value assessment method” (E-P method) as a methodology for assessing the heritage values of buildings and structures or of their parts. The second purpose is to find a sufficiently sensitive process how to avoid invasive diagnostics on the architectural heritage. The procedure is aimed to be applied both on protected and non-protected buildings and structures.

Использование беспилотных летательных аппаратов и ГИС-технологий для определения густоты эрозионной сети водоохранной зоны Белгородского водохранилища

Determining value of erosion network density in the water protection zone is the compulsory index in the automated information system of water bodies state monitoring. The authors of the article developed and tested when studying the Tsimlyansk reservoir water protection zone recommendations for determining erosion network density by materials of distant inspections carried out using pilot-less aircraft (PLA) and tools of geographic information systems (GIS). In the article assessment of erosion network density for the Belgorodsk reservoir water protection zone carried out using given recommendations is presented. Such inspections are especially actual for the banks where regular observation benchmark network is lacking or they have low transport accessibility. Based on series of photographs made by pilotless aircrafts using Agisoft Photo Scan programme relief numerical models and orthophotomaps of the water protection zone are constructed. By direct and indirect signs position of tolwegs for the relief linear erosion forms of different orders—from furrows and grooves to brooks and small rivers. According to the recommendations developed by the authors, the water protection zone is divided into elementary segments and for every of them the value of erosion network density determined using GIS tools. Assessment of erosion network density showed that on the background of general low degree of the relief horizontal dismemberment for the Belgorodsk reservoir water protection zone the reservoir right-bank within Shebekinsky municipal region was distinguished noticeably. The erosion network density of this plot by 5–7 times exceeds the value of this parameter for the whole water protection zone of the reservoir. And only here relief erosion forms fully located within the water protection zone predominate noticeably, that is not characteristic for the rest part e the reservoir cost.

X-Ray Beam Segment Size and Entrance Location Effects on the Integral Quality Monitor (IQM®) Signal and Usefulness in Predicting Complex Segment Output Signals.

Background: The Integral Quality Monitor (IQM®) is an independent online dosimetry device attached to the treatment machine to monitor the accuracy of radiation delivery.Objective: This study investigates the influence of beam segment size and displacement as projected onto the IQM chamber on the signals and determine how individual signals can be added to get a combined segment signal made up of smaller segments.Material and Methods: This is an experimental original research type of study. IQM response maps were generated by irradiating the IQM sensitive area with small elementary segments and measuring their corresponding signals per monitor unit (MU). The output signal/MU was measured for regular and irregular fields and compared with the predicted signal/MU obtained from decomposing the open segment into a set of smaller regular segments and summing their signals from their respective response maps. The dependence of signals on segment size, shape, location and combination was investigated. Results: Predicted signals were calculated within 95-98 % accuracy for regular fields and 90-98% for irregular fields. More uniform fluence contain distribution for larger segments was observed. Response maps were consistent with the geometrical symmetry in the chamber’s wedge shape and the symmetry in the linac fluence. Conclusion: The field decomposition method allows the pre-calculation of known segment output signals per MU within 2% error, although the accuracy drops significantly for smaller, irregular fields. A method of correcting predicted signals in smaller segments needs to be laid down to get a better match with measured signals.

Опыт использования теории риторической структуры для представления логико-когнитивной организации поэтического текста

Rhetorical Structure Theory is popular in theoretical and applied investigations for representing discourse structures and corresponding relational propositions that play the key role in the process of text comprehension. The aim of the article is to explore possibilities and principles of applying the RST for displaying logical and cognitive organization of Russian poetic texts. Driven by the aim of exploring possible applications of RST, its authors and their proponents have analyzed up till now numerous prosaic texts and types of texts. And yet, studying its potential in the field of poetic analysis remains relevant. Since the Theory has never been applied to Russian poetry, an empirical stage of research is necessary. This stage consists in elaborating the principles of dividing a written poetic text into elementary segments, specifying logical relations, constructing structures of poems on this logical basis, completing preliminary analysis of this experience to single out its possibilities and prospects. The article presents the results of such a work. The empirical sample consists of short lyric poems (from 9 to 34 lines); it includes ten texts by A. K. Tolstoy and the same number of texts by I. F. Annensky. The total number of relations, used for representing the structures of these texts, is equal to 26. Frequency ratio of these relations was calculated. Comparative analysis of the poetic structures constructed revealed several differences between the two authors concerning their usage of relations. The results of the investigation evidenced the applicability of Rhetorical Structure Theory to poetry. They show that more research projects in this field are needed to refine its techniques, as well as greater material, including these and other authors, other poetic genres, etc.

Integral quality monitor (IQM®) signal correction factors for small fields to predict larger irregular segment output signals

To develop a method of correcting for the inaccuracies of small adjoined field segments in their contribution to larger fields in order to get a better match between their combined signals and the measured integral quality monitor (IQM) open field signals. This would enable the pre-calculation of known irregular segment output signals per monitor unit (MU), which would be later useful for patient-based dose calculations for treatment verification during pre-treatment treatment validation using the IQM output signal per MU. Small fields exhibit source obscurity and loss of scatter, resulting in smaller signals being measured by the IQM and the subsequent underestimation of IQM output signals of larger segments obtained by combining small segment signals. Larger field segments were broken down into a set of smaller, regular, abutted segments, whose individual signals were added together to get the predicted output signal of the larger field. The signal/MU for each smaller constituent segment was extracted at its exact location from measured IQM response maps, generated by irradiating the IQM with small elementary segments ranging from 1×1cm2 -5×5cm2 , shifting each segment 1cm at a time and measuring its corresponding output signal/MU throughout the entire IQM sensitive area. The predicted signal was weighed against the IQM-measured signal of the open field to calculate a signal correction factor (CF) of each elementary segment size. The CFs were applied to known signals of each set of elementary fields before summation in order to pre-calculate signals of larger irregular fields more accurately. The dependence of CFs on elementary segment size, location of the open field, and beam energy was investigated. CFs exhibited an exponential decrease with increase in elementary segment size. CFs were also invariant with beam energy, changing by ≤1% from 6-15MV. Uncorrected signals for regular fields had relative errors of above 5% whilst signal correction reduced these errors down to ~0.4% (i.e., 99.6% accuracy). For irregular fields, signal correction reduced calculation errors from ~10% to well below 1.5%. Larger signal prediction errors were found when smaller segments were used to reconstruct the field. Open field size and location had a great impact on measured signals but virtually no significance on CFs. Results indicate that summation of small segment signals cannot sufficiently reproduce the same output given by an open field if individual elementary segment signals are not weighted with their respective CFs. This effect is particularly predominant for elementary segments 3×3cm2 and for irregular fields. The method outlined enabled the calculation of signal CFs in order to match predicted signals with measured signals to 98.5% accuracy, thus enabling the pre-calculation of irregular segment output signals/MU for future patient dose calculations.

Fast solution strategy for transient heat conduction for arbitrary scan paths in additive manufacturing

A unique and efficient semi-analytic method is presented for quickly predicting the three-dimensional thermal field produced by conduction from a heat source moving along an arbitrary path. A Green's function approach is used to decouple the solution at each time step into the analytical source contribution and a conduction contribution. The latter is solved numerically using efficient Gaussian convolution algorithms. This decoupling allows for boundary conditions on side boundaries to be satisfied numerically and lowers computational expenses by allowing calculations to be localized around the heat source. The thermal field resulting from arbitrary scan paths is constructed using analytical solutions for elementary linear segments. With focus on efficiency, a novel approach is used to store the calculated analytical line solutions for reuse on multiple other path segments. The results of various scan patterns are presented and successfully verified against finite element simulations. The computational times of predictions are shown to be faster than the corresponding finite element simulation by an order of magnitude with less than 1% average error. Given its ability to quickly predict the thermal history and changes in melt pool geometry due to arbitrary scan paths, this method provides a potentially powerful tool for exploration and optimization of laser powder bed fusion processes.