Ladder Diagrams Research Articles

Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles

We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family of graph building operators Hα for ladder diagrams is constructed and investigated. The complete set of eigenfunctions and the corresponding eigenvalues for the operators Hα are found. This enables us to explicitly express a wide class of four-point ladder diagrams and a general two-loop propagator-type master diagram (with arbitrary indices on the lines) as Mellin-Barnes-type integrals. Special cases of these integrals are explicitly evaluated. A certain class of zig-zag four-point and two-point planar Feynman diagrams (relevant to the bi-scalar D-dimensional “fishnet” field theory and to the calculation of the β-function in ϕ4-theory) is considered. The graph building operators and convenient integral representations for these Feynman diagrams are obtained. The explicit form of the eigenfunctions for the graph building operators of the zig-zag diagrams is fixed by conformal symmetry and these eigenfunctions coincide with the 3-point correlation functions in D-dimensional conformal field theories. By means of this approach, we exactly evaluate the diagrams of the zig-zag series in special cases. In particular, we find a fairly simple derivation of the values for the zig-zag multi-loop two-point diagrams for D = 4. The role of conformal symmetry in this approach, especially a connection of the considered graph building operators with conformal invariant solutions of the Yang-Baxter equation is investigated in detail.

Occam's Razor: Two Arrhythmias in a Single Heart?

Occam's Razor: Two Arrhythmias in a Single Heart?

Implementation of FATEK PLC Based Three Floor Elevator System

The implementation of a low-cost FATEK PLC-based three-floor lift system is described in this study. Elevator systems are critical for vertical mobility in buildings, and their control methods have been revolutionized by the use of programmable logic controllers (PLCs). To control the motion of the lift, we use a DC geared motor. In this example, push buttons are used to direct the elevator to the desired floor. In this scenario, ladder diagram programming was utilized. Because the PLC is easy to programme.

Two-dimensional extended Hubbard model at half-filling

We consider the extended Hubbard model on a two-dimensional square lattice at half-filling. The model is investigated using the strong coupling diagram technique. We sum infinite series of ladder diagrams allowing for full-scale charge and spin fluctuations and the actual short-range antiferromagnetic order for nonzero temperatures. In agreement with earlier results, we find the first-order phase transition in the charge subsystem occurring at v = v c ≳ U/4 with v and U the intersite and on-site Coulomb repulsion constants. The transition reveals itself in an abrupt sign change of a sharp maximum in the zero-frequency charge susceptibility at the corner of the Brillouin. States arising at the transition have alternating deviations of electron occupations from the mean value on neighboring sites. Due to fluctuations, these alternating occupation deviations have short-range order. For the considered parameters, such behavior is found for U ≲ 5t with t the hopping constant. For the insulating case U ≳ 6t, in which the transition is not observed, we find a continuous growth of the Mott gap with v. The evolution of the electron density of states with increasing v is also considered.

First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production

We present new computations for Feynman integrals relevant to Higgs plus jet production at three loops, including first results for a non-planar class of integrals. The results are expressed in terms of generalised polylogarithms up to transcendental weight six. We also provide the full canonical differential equations, which allows us to make structural observations on the answer. In particular, we find a counterexample to previously conjectured adjacency relations, for a planar integral of the tennis-court type. Additionally, for a non-planar triple ladder diagram, we find two novel alphabet letters. This information may be useful for future bootstrap approaches.

Improved quasiparticle self-consistent electronic band structure and excitons in β−LiGaO2

The band structure of $\beta$-LiGaO$_2$ is calculated using the quasiparticle self-consistent QS$G\hat W$ method where the screened Coulomb interaction $\hat W$ is evaluated including electron-hole interaction ladder diagrams and $G$ is the one-electron Green's function. Improved convergence compared to previous calculations leads to a significantly larger band gap of about 7.0 eV. However, exciton binding energies are found to be large and lead to an exciton gap of about 6.0 eV if also a zero-point-motion correction of about $-0.4$ eV is included. These results are in excellent agreement with recent experimental results on the onset of absorption. Besides the excitons observed thus far, the calculations indicate the existence of a Rydberg-like series of exciton excited states, which is however modified from the classical Wannier exciton model by the anisotropies of the material and the more complex mixing of Bloch states in the excitons resulting from the Bethe-Salpeter equation. The exciton fine structure and the exciton wave functions are visualized and analyzed in various ways.

Toward precision Fermi-liquid theory in two dimensions

The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an effective field theory framework. It has long been observed that universal corrections to the energy density to two orders in the interaction strength do not agree with Monte Carlo simulations in the weak-coupling regime. Here, universal corrections to three orders in the interaction strength are obtained for the first time, and are shown to provide agreement between theory and simulation. Special consideration is given to the scale ambiguity associated with the non-trivial renormalization of the singular contact interactions. The isotropic superfluid gap is obtained to next-to-leading order, and nonuniversal contributions to the energy density due to effective range effects, p-wave interactions and three-body forces are computed. Results are compared with precise Monte Carlo simulations of the energy density and the contact in the weakly-coupled attractive and repulsive Fermi liquid regimes. In addition, the known all-orders sum of ladder and ring diagrams is compared with Monte Carlo simulations at weak coupling and beyond.

A compact multi-functional model of the rabbit atrioventricular node with dual pathways.

The atrioventricular node (AVN) is considered a "black box", and the functioning of its dual pathways remains controversial and not fully understood. In contrast to numerous clinical studies, there are only a few mathematical models of the node. In this paper, we present a compact, computationally lightweight multi-functional rabbit AVN model based on the Aliev-Panfilov two-variable cardiac cell model. The one-dimensional AVN model includes fast (FP) and slow (SP) pathways, primary pacemaking in the sinoatrial node, and subsidiary pacemaking in the SP. To obtain the direction-dependent conduction properties of the AVN, together with gradients of intercellular coupling and cell refractoriness, we implemented the asymmetry of coupling between model cells. We hypothesized that the asymmetry can reflect some effects related to the complexity of the real 3D structure of AVN. In addition, the model is accompanied by a visualization of electrical conduction in the AVN, revealing the interaction between SP and FP in the form of ladder diagrams. The AVN model demonstrates broad functionality, including normal sinus rhythm, AVN automaticity, filtering of high-rate atrial rhythms during atrial fibrillation and atrial flutter with Wenckebach periodicity, direction-dependent properties, and realistic anterograde and retrograde conduction curves in the control case and the cases of FP and SP ablation. To show the validity of the proposed model, we compare the simulation results with the available experimental data. Despite its simplicity, the proposed model can be used both as a stand-alone module and as a part of complex three-dimensional atrial or whole heart simulation systems, and can help to understand some puzzling functions of AVN.

SIMULATION OF THE TRAJECTORY OF AN ELECTRIC WHEELCHAIR CONTROLLED THROUGH PROGRAMMABLE LOGIC CONTROLLER AND HMI

This paper presents a software module made by means of a programmable logic controller and an HMI (Human Machine Interface), designed to control the movement of an electric wheelchair. By developing this module, a major advantage is offered to people with disabilities, who have movement difficulties. By implementing this command on a wheelchair, people can move independently using this machine that can be controlled from a touch screen. In this direction, the user has the possibility to choose the following directions of movement of the car: forward-backward and left-right, as well as the possibility to impose the speed of movement. The software program was created using ladder diagram language, and the user interface is provided through an HMI.

Syncope After Transcatheter Aortic Valve Implantation: Pace or Not?

Syncope After Transcatheter Aortic Valve Implantation: Pace or Not?

Plc-Based Starter Generator Set Automation Simulation

Maintenance of the generator set is very influential on the performance of an electric power supply. Especially in a vital institution such as a hospital. The existence of a generator is very necessary as an anticipation if the electricity supply from PLN experiences a trip. Limited time and energy are the main factors underlying the lack of generator maintenance, so generators often fail when needed. Starting from the limited time and energy, the idea emerged about the need for a software that is able to control the system automatically so that it can heat up the generator engine at any given time. Programmable logic controller (PLC) is a program that is used to operate an automatic generator set system. The command made in the form of an image that can be interpreted as a logic circuit command is called a ladder diagram. The command taken from the input signal is a switch and the output signal command is a load. The output signal in this machine is a motor which is analogous to a generator, based on the logic in the generator. When input 0001 is turned on, the timer 001 will count down 25 seconds. Once fulfilled it will start the motor, if for 3 seconds the motor does not start, it will activate the 004 team as a delay before the system starts trying to start again. If in 3 times the motor is started it still won't turn on, it will activate address 1004. Address 1004 itself is an alarm that will give a warning if the system cannot function normally and must get further checks. According to the results above, the use of software using CPM 1A can be said to have been successfully applied to simulations, but there will be significant shortcomings if it is applied for public use, due to the maximum time setting of only 16 minutes, while public use requires flexibility in the application of appropriate time settings. with the field of application. Based on the observations, it can be concluded that the initial purpose of the concept of making tools is fulfilled by the realization of a simulation. The use of PLC is very suitable to be applied to automating generator sets, but the simulation performance has not been maximized due to limited capabilities in developing PLC software timer applications. however, there will be significant drawbacks if applied for public use, due to the maximum time setting of only 16 minutes, while for public use requires flexibility in the application of time settings according to the field of application. Based on the observations, it can be concluded that the initial purpose of the concept of making tools is fulfilled by the realization of a simulation. The use of PLC is very suitable to be applied to automating generator sets, but the simulation performance has not been maximized due to limited capabilities in developing PLC software timer applications. however, there will be significant drawbacks if applied for public use, due to the maximum time setting of only 16 minutes, while for public use requires flexibility in the application of time settings according to the field of application. Based on the observations, it can be concluded that the initial purpose of the concept of making tools is fulfilled by the realization of a simulation. The use of PLC is very suitable to be applied to automating generator sets, but the simulation performance has not been maximized due to limited capabilities in developing PLC software timer applications. while the use for the public requires flexibility in the application of time settings in accordance with the field of application. Based on the observations, it can be concluded that the initial purpose of the concept of making tools is fulfilled by the realization of a simulation. The use of PLC is very suitable to be applied to automating generator sets, but the simulation performance has not been maximized due to limited capabilities in developing PLC software timer applications. while the use for the public requires flexibility in the application of time settings in accordance with the field of application. Based on the observations, it can be concluded that the initial purpose of the concept of making tools is fulfilled by the realization of a simulation. The use of PLC is very suitable to be applied to automating generator sets, but the simulation performance has not been maximized due to limited capabilities in developing PLC software timer applications.

A Novel Method for Converting Colored Petri Nets to Ladder Diagram in the Automation of Automated Manufacturing Systems

The Ladder Diagram (LD) is an industry-standard programming language for constructing automated manufacturing systems (AMSs) control algorithms. Petri net (PN) theory, on the other hand, is a mathematical and graphical modeling tool for AMSs. Multiple types of PN-based LDs are designed for AMSs with highly complicated LD structures. Thus, it is necessary to propose a technique that can assist in the minimization of the structural complexity of LDs. The main purpose of this study is to propose a methodology for the implementation of LDs in AMSs. First, a colored resource-oriented Petri net (CROPN) is developed for modeling and guaranteeing the deadlock-free behavior of AMS. Second, a ladder diagram CROPN (LDCROPN) is constructed in order to transform the CROPN into an LD. The proposed LDCROPN is assessed using instances from the literature. The results show that the LDCROPN is effective, has a simpler structure, and has less computational overhead than existing techniques.

Developing Program Code for Automatic Color Code Sensing Punching Machine Using WPL Software

This paper presents the idea of developing a logic or program code for an Automatic Color code sensing and punching machine which is driven based on Pneumatic architecture and can be used at the packing section in industries where the end user can punch labels on the objects which are moving on the conveyor based on their color. The program code basically controls the Pneumatic valves present in the system which actuates the Cylinders and helps in clamping and de clamping of moving objects and henceforth achieving the label at the required spot, whereas the desired color is acquired from the dedicated color sensor which helps in deciding the labeling process. This paper uses the advanced industrial controller (PLC) software called WPL Soft which is the most widely used tool in industries. This software requires a dedicated programming language called Ladder diagram, which is the 80% preferred programming language worldwide for programming PLCs. A program has been developed for automatically creating the application for color sensing and punching label on the desired objects based on color.

Petri net models of discrete logics used in control algorithms developed in ladder diagram language

Petri net models of discrete logics used in control algorithms developed in ladder diagram language

On self-energy contributions near Berezinskii–Kosterlitz–Thouless transition in interacting homogeneous 2D Bose system

ABSTRACT We explore the consequences of including quantum corrections in an interacting 2D Bose system near Berezinskii–Kosterlitz–Thouless (BKT) transition. To go beyond mean-field theory and treat correlations, we use Matsubara Green's function method, and, following a previous novel approach, study features of the interacting Green's function just above the transition. We numerically obtain self-consistent solutions of boson self-energy to second order as well as higher order (re-summation of ladder and bubble diagrams) in the interaction strength, for the entire range of momentum, k, and compare our findings with analytic results in the limits of low- and high-k. Thereby, in the weak interaction limit, we retrieve the universal transition condition and calculate the universal scaling parameter (independent of interaction strength). The renormalised single-particle Green's function is found to decay algebraically at large distance r.

Ultracold spin-balanced fermionic quantum liquids with renormalized P -wave interactions

We consider a spin-balanced degenerate gas of spin-1/2 fermions whose dynamics is governed by low-energy $P$-wave interactions, characterized by the scattering volume $a_1$ and effective momentum $r_1$. The energy per particle $\bar{\cal{E}}$ in the many-body system is calculated by resumming the ladder diagrams comprising both particle-particle and hole-hole intermediate states, following the novel advances recently developed by us in Ann.Phys. 437,168741(2022). This allows to obtain a renormalized result for $\bar{\cal{E}}$ within generic cutoff regularization schemes, with $\bar{\cal{E}}$ directly expressed in terms of the scattering parameters $a_1$ and $r_1$, once the cut off is sent to infinity. The whole set of possible values of $a_1$ and $r_1$ is explored for the first time in the literature looking for minima in the energy per particle with $\bar{\cal{E}}$ given as described. They are actually found, but a further inspection reveals that the associated scattering parameters give rise to resonance poles in the complex momentum-plane with positive imaginary part, which is at odds with the Hermiticity of the Hamiltonian. We also determine that these conflictive poles, with a pole-position momentum that is smaller in absolute value than the Fermi momentum of the system, clearly impact the calculation of $\bar{\cal{E}}$. As a result, we conclude that unpolarized spin-1/2 fermionic normal matter interacting in $P$-wave is not stable. We also study three universal parameters around the unitary limit. Finally, the whole set of values for the parameters $a_1$, $r_1$ is characterized according to whether they give rise to unallowed poles and, if so, by attending to their pole positions relative to the Fermi momentum of the system explored.

PEMANFAATAN ARDUINO NANO V5 DALAM MERANCANG PROGRAMABLE LOGIC CONTROL

Programmable Logic Control or PLC is the control of a microprocessor for industry, especially in the field of automation, which functions as an alternative to mechanical relays used in controlling complex or complex processes. Programmable Logic Control, in general, has a relatively high price, and not everyone can learn it. For this reason, Arduino nano is used for Programable Logic Control V5. Selection of the method utilized literature study of the relevant scientific literature as reference material. Utilization of Arduino Nano V5 in designing Programmable Logic Control by analyzing and assembling starting from input devices, process devices, and output devices. For the programming method of Programable Logic Control ladder diagrams based on Arduino Nano V5 using Outseal Studio Software. For the hardware (hardware), use the input, namely the Push Button, while for the output device, namely the magnet contractor, as a direct on line (DOL) simulation module.

IMPLEMENTASI PROGRAMMABLE LOGIC CONTROL (PLC) OMRON CP1E PADA SISTEM KENDALI MOTOR INDUKSI STAR-DELTA UNTUK KEBUTUHAN INDUSTRI

The star delta control circuit is a sistem used to control an induction motor with a minimum power of 7.5 kW. Most industries still use conventional control sistems or without the use of PLC (Programmable Logic Controller). The purpose of this research is to apply PLC (Programmable Logic Controller) OMRON CP1E E-30-DR-A as an automatic control sistem on a star delta induction motor, whose working sistem is designed using a ladder diagram. In this study also added a safety sistem that will provide more protection to the components and the sistem as a whole. The main components of the PLC used have a working voltage range of 100 - 240 VAC. The design of this sistem uses two main sistems, namely a control sistem consisting of an ON/OFF pushbutton with a working voltage of 24 VDC. The power sistem consists of a contactor with a working voltage at terminal A1 of 220 VAC and a manual motor starter as a safety for the induction motor. The results of testing this sistem show that all sistem components can function properly with a supply voltage according to specifications, namely the working voltage at the L1 PLC terminal is 241.1 VAC, the voltage on the ON pushbutton control sistem is 24.53 VDC and the OFF pushbutton is 24,6 VDC. The working voltage on the power sistem at the contactor A1 terminal is 241.1 VAC.

Software Design of VerilogHDL Code Generation for Ladder Diagram and Data Acquisition Using LABVIEW

Powerful advantages of programmable logic controller (PLC) dominate process industries. Scan time of PLC increases with the number of inputs, rungs added in ladder diagram (LD). Researchers have identified and proved that field programmable gate array (FPGA) is more suitable than PLC for high speed applications. PLC executes the instructions represented through LD. PLC programmers are not familiar with FPGA programming. But, FPGA does not support LD based programming. This work has developed application software to generate equivalent VerilogHDL code for LD using LabVIEW. Novelty in this work is that each rung is defined using an "assign" statement which helps simultaneous execution of all the rungs. A data acquisition system was created to monitor the digital signals handled by the FPGA. The software was verified with a case study of substances mixing and traffic light control system.

Normal state of attractive Fermi gases from coupled-cluster theory

We introduce coupled-cluster (CC) theory for the numerical study of the normal state of two-component, dilute Fermi gases with attractive, short-range interactions at zero temperature. We focus on CC theory with double excitations (CCD) and discuss its close relationship with -- and improvement upon -- the t-matrix approximation, i.e., the resummation of ladder diagrams via a random-phase approximation. We further discuss its relationship with Chevy's variational wavefunction ansatz for the Fermi polaron and argue that CCD is its natural extension to nonzero minority species concentrations. Studying normal state energetics for a range of interaction strengths below and above unitarity, we find that CCD yields good agreement with fixed-node diffusion Monte Carlo. We find that CCD does not converge for small polarizations and large interaction strengths, which we speculatively attribute to the nascent instability to a superfluid state.