Abstract
Emotions are commonly considered to be the most expressive of everyday human experiences, giving a sense of fullness and reality of life. The ability to recognize human emotions as a manifestation of higher intelligence is desirable feature. There are several models of emotional experience that can become the basis for building a universal emotional recognition system. In this article, we check the correctness of the designed emotional model. We check the evaluation of the system’s operation by human observers.
1 Introduction
According to the latest psychological knowledge [1], emotional systems are located in older evolutionary regions of the brain and are mostly homologous in all mammals; also in all mammals, the chemistry of these systems is similar. Emotional systems generate instinctive behavioral responses that are closely related to the primary affections that accompany these responses. In principle, all emotional systems are linked to the system responsible for what we call motivational processes in psychology, i.e., the search system. It stands out from the rest by the fact that it takes part in basically every action of the body that is directed toward the goal [2]. By analogy, it can be assumed that the development of emotion models should contribute to a significant improvement in the search of space by artificial intelligence (AI), above all, to an adequate response and correct decision-making. Computer simulations of psychological phenomena have a half-century history. The following research was aimed at introducing an emotional model that will make the AI movement be interpreted as emotional behavior. This approach will allow to check if the emotional model in AI can be correctly interpreted by humans [3]. The application of the developed model can be used in both computer games [4] and robotics. Developed location models [5] can be enriched with this models. Researchers try model some emotions to a robot or a virtual agent. The respective systems can be called computational systems of emotions. In this article, we concerns the issue of recognizing emotions, in which the latest solutions are able to identify and classify emotions based on agents’ movements.
2 Emotion engines and theories
Emotion engines are adaptations of models describing appraising of events and processing temporal emotional state. These are based on three main theories: PAD space, appraisal theory, and PSI schema. Each of those originate from the evaluation of psychological research regarding emotions. Difference between those mainly focus around interpretation of emotional state processing. The main common aspect of all ideas is a division of elements that have influence on the emotional state. Besides events in outer environment, the emotional state depends on the character of a unit and a current mood. Depending on the considered theory, additional aspects of the appraisal process are included, for example, social aspect or cultural aspect [6,8,10,14,17].
2.1 PAD space
PAD space (based on Mehrabian works) assumes emotion to be point in a three-dimensional space based on three aspects. That is why point or emotion, as it can be understood, may be called composition of space parameters, where the space itself is considered in range between −1 and 1 in each dimension. Dimensions or parameters are pleasure, arousal, and dominance. In this case, the emotional state of a unit is activated or changed by events in surrounding and degradation of activation over time. These changes are based on shifts in the PAD space. Each activation causes deviation in relation to the beginning of PAD space and degradation rapprochement to it. Good example is eating a meal. It is an event that has pleasant characteristic and at the same time needs activation in the direction of focusing on processing of taste and experience itself.
Understanding of the emotional state as a point in the PAD space allows for simple mapping results of emotion engines based on other theories. Model using the PAD space theory is Wasabi. This model describes overall architecture of an engine, which explains dynamics of emotional state processing. Figure 1 shows the structure of an engine based on the Wasabi model [10].

Scheme of Wasabi architecture with distinction of components, where Tick is processors tick and Knowledge is understanding if environment characteristics.
Distinctive part of this engine is parametrization of the emotional state. The main assumption of this architecture is, as mentioned earlier, kept and simulated as point in 3D space. IT depends on three degrees-of-freedom called valence, mood, and boredom. It is additional space correlated and placed between PAD emotional state and event processing. It is used to decide on event’s dynamics and its influence on unit’s state. In the next step to describe the emotional state in an unambiguous way for a user, VMB point is mapped to point in the PAD space. Emotion’s value is decided based on the distance of an emotional state from distinct emotions, since each of particular emotions has defined place in the PAD space.
2.2 Appraisal theory
It is the most popularly used theory in models describing the emotional state interpretation and processing. The basis of this approach is assumption, that, emotion depends on a pattern of individual appraisal regarding event assembled from relation among individual thoughts, intentions, and desires, which is known also as human–environment relation. This relation was formalized in the shape of appraising variables, explaining the meaning of an event for a unit. Hence, in this theory, emotions are the result of direct appraisal of an event done by an individual unit. The most used model that uses this idea is OCC model (from authors names, Ortony, Clore, and Collins)
This model characteristics is event appraisal done based on, event’s attributes, origin of event as well as environment in which it happened. Appraisal itself is built on defined criteria in effect of which emotional state could be received. Attributes of an event are bound with relation of deliberating unit with event itself. What could be understood as what consequences an event has to the unit or how the origin of an event is related to the unit. In other words, unit must check if an event was positive or negative and how an environment reacts. Figure 2 describes schema of the OCC analysis [10,12,13].

Scheme of the OCC model explaining deliberative stage of emotional state creation.
Perfect example of practical use can be FAtiMA engine (FearnotAffective Mind Architecture). Its characteristic point is layered design, where each layer considers other aspect of event’s appraisal. The most vital one is the deliberative component, which in fact ensures engagement of the main appraisal process of the incoming data. The result of this appraisal is certain emotional state, which is then taken under consideration during decision-making about further unit’s actions. Emotional state is presented as floating values in scale between 0 and 1. Knowledge module also plays an important role, defining knowledge about environment and explaining relation to observed events. It is described in Figure 3.

Scheme of FATiMA with additional layer distinction.
2.3 PSI theory
PSI theory, which name comes from Greek letter associated with psychology, is based on assumption, that is, emotional state in relation to event depends on the level of needs realization, according to the basis of Maslow’s needs pyramid. To be exact, actions and reactions of considered unit are dictated by motivations, which emerge from need to fulfill needs. Depending on the priority, agent or unit strive to the homeostasis state trying to fulfill each of the mentioned needs. Starting from primary needs, like security, ending on the most sophisticated like social relations. Therefore, from needs motivations emerge, which cause changes in the level of aims realization. Aims with consideration of the emotional state resulting from event appraisal give possibility to decide about further steps of an agent. This theory is used by a model with the same name. Figure 4 describes an engine architecture created based on this model [9].

Scheme of PSI architecture.
2.4 Hybrid approach
There are also hybrid models getting inspiration from multiple theories. Good example can be SIMPLEX. It uses appraisal theory like in OCC model during event appraisal and PAD space to interpret and store the emotional state. It is described in Figure 5 [10].

Scheme of SIMPLEX architecture.
There is also other idea of assembling PSI and appraisal theories and many other, but differences coming from assembling are not very important to distinct them in comparison to the main theories. In addition, those do not have implementation that could be verified and compared with existing solutions.
3 Emotions in navigation
Emotion engines have use in the area of pathfinding. There are several methods of adaptation into existing heuristic solutions as well as into machine learning modules used for adaptive navigation.
Example can be the particle system used in eCology simulation. It is based on two main aspects. First aspect is treating a moving unit or an agent as a particle owning velocity and mass. Through these attributes, the agent can be attracted or repelled by different objects in virtual environment. Second aspect is the use of engine emotion to define relation with objects in the area, in that way appraising if one should be attractor or repel considered agent and with what force. Depending on events in surrounding, like giving food or shouting, agent might avoid one object or approach other. Figure 6 illustrates the idea [15].
![Figure 6
Scheme explaining attractor–repeller system [18].](/document/doi/10.1515/phys-2020-0199/asset/graphic/j_phys-2020-0199_fig_006.jpg)
Scheme explaining attractor–repeller system [18].
Similar solution can be used as augmentation of pathfinding algorithms based on heuristics. Using emotional state and the source of emotional change trespassing cost is changed near it, and thus adapting direction of path search. Algorithm will find the way with emotional state reasoning.
Another way to use the emotional state in pathfinding are emotional maps. Similar to the example of earlier solution, this one also manipulates trespassing cost through certain areas. However, aspect which distincs this idea from others is storing data consisiting of connection between position and emotional state, in separate data collection. Thus, forming abstract map of relation reffering to emotion states and its bounding with certain areas. It is treated as abstractive layer, in which data are compared and mapped to real graph of path search. In addition, in emotion maps, there is no necessity to connect emotional state if object in environment. Event in certain area causes emotional state change in emotional map, which is also influenced by degradation over time. For instance, whenever something odd happen in one place in environment, like explosion or scream, it gets registered in emotional map as hazardous area with higher trespassing cost. If in near future nothing happens, this effect will decrease over time. Figure 7 presents visualisation of this effect [7].
![Figure 7
Scheme explaining degradation process of tresspassing cost [15,18].](/document/doi/10.1515/phys-2020-0199/asset/graphic/j_phys-2020-0199_fig_007.jpg)
Scheme explaining degradation process of tresspassing cost [15,18].
There are approaches to bound emotion engine with machine learning aiming to research influence of emotions on learning process of an agent during maze walking through. Emotion engine is a thruster of awarding and penalizing during tries of getting through a maze. In case of finding dead-end or staying in maze for too long, what changes its arousal level and valence in VMB space, which is further mapped to the emotional state imitating fear and frustration. This results with reinforcing learning effect in the direction of earlier trials. Where in opposite case, relief and satisfaction would be acquired with quick passing through the mentioned maze. This way, positive effect reinforces optimization of path through maze [11].
4 Proposed emotion engine
Based on FATiMA engine, the proposal of emotion engine was introduced. It consists of single internal layer (deliberative layer), allowing to do appraisal of an event according to OCC model rules. Although in contradiction to appraisal theory assumption, it is settled that overall emotional state can be reduced to five basic emotions: anger, fear, sorrow, disgust, and joy. Those were settled as basic by Ekman’s work in this field. According to his theory, each emotion is just composition with different levels of feeling of those basic emotions. This way, assuming scale of feeling range between 0 and 1 for each of basic emotions, and emotional state can be defined. Through this assumption, amount of considered emotions is reduced from 22 to 5. It highly simplifies architecture. Another step taken was translating emotions to PAD space according to the PAD space theory. This allowed comparison of emotional state with other solutions.
Besides storing and processing of the emotional state, there is a need to define methods of translating emotion engines results into reactions. The area of pathfinding used correlation between reaction tendencies and emotions based on the study by Shen and Bigsby. It was noticed that that most of psychological theories connected with emotions agree with certain behaviors to originate from emotions (for example, of the studies by Scherer, Lazarus, Frijida, Dillard, Russell, Johnstone, Schorr, and many others). This aspect is presented in Table 1 [16].
Listing of relations between emotions and tendencies [16]
Emotion | Relational theme | Valence | Function | Action tendency |
---|---|---|---|---|
Surprise | Novel stimuli | Open | Orient | Allocate attention |
Anger | A demeaning offense against me and mine | Negative | Remove obstacle | Attack/reject |
Fear | Facing uncertain, existential threat/danger | Negative | Protection | Revise existing plan/create new plan |
Sadness | Having experienced an irrevocable loss | Negative | Learning/recuperation | Review plan/convalesce |
Guilt | Having transgressed a moral imperative | Negative | Self-sanction | Strive to attain standard |
Disgust | Taking in or being too close to an indigestible object or idea | Negative | Maintain gustatory goal | Reject substance/withdraw |
Happiness | Making reasonable progress toward the realization of a goal | Positive | Self-reward | Bask/bond |
Treating fear as example, processing of emotion into reaction can be presented. If event recorded by an agent is new, nothing similar happened earlier, and it caused existential danger, then it shall be treated as negative. This causes immediate decrease of positive emotion value. Moreover, that kind of event causes fear of loosing life (assuming typical reaction of human, not considering psychological deviation). Reaction function in this case is chosen as protective aiming elimination or reducing the danger. It assumes revision of the current plan and proposing new action. In other words, this process can be explained on example scenario. Assuming that an agent is moving in the direction of certain goal and approaching a danger, it will try to change the moving direction allowing to keep distance from the source of fear. Velocity of an agent will be also changed to decrease necessary contact with the hazardous area. Depending on the level of danger, goal itself could also be revised and make agent to resign of pursuing it.
To create such correlation, behavioral tree was used, which defines set of actions fitting emotions. Thus, the priority choice of action was stated based on dominating emotion and level of its activation. Level of activation also plays a role in decision-making, causing escalation or de-escalation of actions. This kind of approach allows simple adaptation of engine with many different NPC (none-player character) steering systems. Except of simplicity in adaptation, correlating emotion engine with behavioral tree greatly increases possibilities of the extending proposed solution with additional actions, without losing preferences of emotional state processing.
Moreover, solution includes emotional maps and particle system adaptation to ensure wider influence on pathfinding. Therefore, the system of trespassing costs was introduced with the degradation of effect over time and repeller–attractor attribute. In addition, the area of activation is also changed based on event interpretation. To verify the correctness of approach and proposed solution, test was conducted checking readability of NPC behavior by possible participant or user of simulation.
5 Architecture of testing environment
Conducted experiment was done with the use of UnrealEngine since it has wide choice of tools, which highly simplifies and accelerates implementation. It also has built-in pathfinding system that uses the heuristic algorithm. In addition, it considers cost of trespassing, and blueprints system can be easily used to create behavioral trees. Finally, there is a wide support of graphical aspect for many kinds of tests in virtual environment.
Test was conducted in the form of survey, in which users decided about readability of agents reactions in virtual environment. To reduce any possible interferences and reasons of biased judging, agent and other elements were presented as 2D geometrical figures according to following illustration. Agent, represented as a triangle, has a task of getting through a maze. Green circle represents emotional stimuli. Depending on the trial, different emotions are stimulated, which changes the behavior of the agent. User is supposed to decide which emotion is dominating decisions of triangle.
6 Test
Thirty-four people participated in the test of various age. Exact scenario of test is presented as follows:
Each participant was presented with 6 recordings. One recording for one emotional reaction (joy, anger, disgust, sad, and fear) and additional reference HreHcording without emotion engine influence
Recording 1: after seeing stimuli (green circle), triangle moved away in opposite direction (run away) – fear
Recording 2: after seeing stimuli (green circle), triangle moved slowly in the direction toward stimuli and stayed in a close range and then continued the movement to its goal – joy
Recording 3: after seeing stimuli (green circle), triangle moved around stimuli, keeping distance, in a quick manner – disgust
Recording 4: after seeing stimuli (green circle), triangle very quickly approached stimuli and then moved to its goal (attack) – anger
Recording 5: after seeing stimuli (green circle), triangle very slowly moved toward its goal, ignoring stimuli – sad
Recording 6: after seeing stimuli (green circle), triangle moved with typical velocity to its goal – reference recording
Every participant was asked to decide what emotion is presented, where multiple answer was allowed
After first stage, participants were requested to connect emotions with description of reactions, where multiple answers were also allowed.
Last stage was asking participants to judge reactions again, with changed order of recordings to check if stage 2 had learning aspect
7 Results
Following are the results of test (Figure 8).

Results of the first stage during tests.
Every dominating emotion was correctly recognized. However, participants were not sure of their answers. It is visible on example of recording 2 and 4. Clearly anger and joy were thought to be similar. Probable reason is high level of activation in expressing both emotions. Both are distinct with impulsive and sudden actions, in comparison with other emotions. Clear recognition appeared for disgust, where great majority assumed the origin of behavior. In addition, reference recording also proved to be easily recognizable what seem to proof correctness of testing scenario.
Second stage results are presented in Table 2.
Results of correlating behavior descriptions with emotions
* | Attack | Interest | Slow movement | Running away | Omitting |
---|---|---|---|---|---|
Anger | 30 | 0 | 2 | 3 | 3 |
Joy | 5 | 34 | 2 | 0 | 0 |
Sadness | 0 | 1 | 22 | 6 | 9 |
Fear | 2 | 1 | 7 | 25 | 12 |
Disgust | 2 | 0 | 12 | 6 | 25 |
Participants placed descriptions clearly correctly. However, the highest doubts were with slow movement, where a few interviewees seen disgust. Sadness and disgust had the most similar results.
Here are results of the last stage (Figure 9).

Results of last stage during tests.
Judging result in last stage shows much higher certainty in choices what could be understood, as increase in emotion recognition. It would mean that second stage had learning characteristic for participants.
8 Conclusions
During research emotion, engine was created, which connects the appraisal theory and the PAD space theory, allowing to increase adaptation possibilities. In addition, complexity of engine architecture was decreased based on Ekman’s theory with keeping dynamics of emotional state processing. Next behavioral tree was included as augmentation of emotion engine aiming to define quantifiable collection of actions and mechanics of decision-making. The reason was to correlate it with emotion engines steering abilities. Hybrid solution that was created greatly increases the number of possibilities to use it in virtual environment and crowd simulations. It should also increase the potential of user’s immersion during experiments checking human behavior in crowd for different scenarios. Hence, it can lower the possible cost of such experiment substituting the majority of participants with NPC units. Moreover, with use of emotion-tendency correlation, collection of actions was created and defined, which can be assigned to the emotional state, resulting from engine processing, depending on the currently dominating emotion and its level. This way reasonable decision system was acquired with adaptation of predictable behavior, including basis in the research of psychology field. Finally, there was a try to verify the accuracy of chosen approach and chosen actions in the direction of users understanding agent’s acting. It was done on the basis of moving aspect. Results proved to correct user’s understanding of agent’s emotional state observing its behavior. However, some of emotions and actions seemed to have similar impressions. The reason might be similarity between emotions in aspect of the activation level. Moreover, it is highly probable that some of emotions need additional ways of expression, like body expression. Therefore, some additional tests should be conducted with animations included. Field of emotion simulation in virtual environment has the wide use of potential, especially in crowd simulations in which the user is supposed to feel immersion and adapt to groups actions. Further research will focus on this aspect. This work was supported by the NCBiR under Project POIR.01.02.00-00-0133/16.
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© 2020 Marcin Daszuta et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
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- Influence of modern magnetic and insulation materials on dimensions and losses of large induction machines
- New emotional model environment for navigation in a virtual reality
- Performance comparison of axial-flux switched reluctance machines with non-oriented and grain-oriented electrical steel rotors
- Erratum
- Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”
Articles in the same Issue
- Regular Articles
- Model of electric charge distribution in the trap of a close-contact TENG system
- Dynamics of Online Collective Attention as Hawkes Self-exciting Process
- Enhanced Entanglement in Hybrid Cavity Mediated by a Two-way Coupled Quantum Dot
- The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions
- Diagnostic model of low visibility events based on C4.5 algorithm
- Electronic temperature characteristics of laser-induced Fe plasma in fruits
- Comparative study of heat transfer enhancement on liquid-vapor separation plate condenser
- Characterization of the effects of a plasma injector driven by AC dielectric barrier discharge on ethylene-air diffusion flame structure
- Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid
- Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model
- Novel numerical analysis for nonlinear advection–reaction–diffusion systems
- Heuristic decision of planned shop visit products based on similar reasoning method: From the perspective of organizational quality-specific immune
- Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel
- Dynamic triaxial constitutive model for rock subjected to initial stress
- Automatic target recognition method for multitemporal remote sensing image
- Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method
- Adaptive magnetic suspension anti-rolling device based on frequency modulation
- Dynamic response characteristics of 93W alloy with a spherical structure
- The heuristic model of energy propagation in free space, based on the detection of a current induced in a conductor inside a continuously covered conducting enclosure by an external radio frequency source
- Microchannel filter for air purification
- An explicit representation for the axisymmetric solutions of the free Maxwell equations
- Floquet analysis of linear dynamic RLC circuits
- Subpixel matching method for remote sensing image of ground features based on geographic information
- K-band luminosity–density relation at fixed parameters or for different galaxy families
- Effect of forward expansion angle on film cooling characteristics of shaped holes
- Analysis of the overvoltage cooperative control strategy for the small hydropower distribution network
- Stable walking of biped robot based on center of mass trajectory control
- Modeling and simulation of dynamic recrystallization behavior for Q890 steel plate based on plane strain compression tests
- Edge effect of multi-degree-of-freedom oscillatory actuator driven by vector control
- The effect of guide vane type on performance of multistage energy recovery hydraulic turbine (MERHT)
- Development of a generic framework for lumped parameter modeling
- Optimal control for generating excited state expansion in ring potential
- The phase inversion mechanism of the pH-sensitive reversible invert emulsion from w/o to o/w
- 3D bending simulation and mechanical properties of the OLED bending area
- Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics
- The measure of irregularities of nanosheets
- The predicted load balancing algorithm based on the dynamic exponential smoothing
- Influence of different seismic motion input modes on the performance of isolated structures with different seismic measures
- A comparative study of cohesive zone models for predicting delamination fracture behaviors of arterial wall
- Analysis on dynamic feature of cross arm light weighting for photovoltaic panel cleaning device in power station based on power correlation
- Some probability effects in the classical context
- Thermosoluted Marangoni convective flow towards a permeable Riga surface
- Simultaneous measurement of ionizing radiation and heart rate using a smartphone camera
- On the relations between some well-known methods and the projective Riccati equations
- Application of energy dissipation and damping structure in the reinforcement of shear wall in concrete engineering
- On-line detection algorithm of ore grade change in grinding grading system
- Testing algorithm for heat transfer performance of nanofluid-filled heat pipe based on neural network
- New optical solitons of conformable resonant nonlinear Schrödinger’s equation
- Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model
- Circularly symmetric algorithm for UWB RF signal receiving channel based on noise cancellation
- CH4 dissociation on the Pd/Cu(111) surface alloy: A DFT study
- On some novel exact solutions to the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky system arising in physical science
- An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation
- Mining reasonable distance of horizontal concave slope based on variable scale chaotic algorithms
- Mathematical models for information classification and recognition of multi-target optical remote sensing images
- Hopkinson rod test results and constitutive description of TRIP780 steel resistance spot welding material
- Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient
- Analytical solution of one-dimensional Pennes’ bioheat equation
- MHD squeezed Darcy–Forchheimer nanofluid flow between two h–distance apart horizontal plates
- Analysis of irregularity measures of zigzag, rhombic, and honeycomb benzenoid systems
- A clustering algorithm based on nonuniform partition for WSNs
- An extension of Gronwall inequality in the theory of bodies with voids
- Rheological properties of oil–water Pickering emulsion stabilized by Fe3O4 solid nanoparticles
- Review Article
- Sine Topp-Leone-G family of distributions: Theory and applications
- Review of research, development and application of photovoltaic/thermal water systems
- Special Issue on Fundamental Physics of Thermal Transports and Energy Conversions
- Numerical analysis of sulfur dioxide absorption in water droplets
- Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part I
- Random pore structure and REV scale flow analysis of engine particulate filter based on LBM
- Prediction of capillary suction in porous media based on micro-CT technology and B–C model
- Energy equilibrium analysis in the effervescent atomization
- Experimental investigation on steam/nitrogen condensation characteristics inside horizontal enhanced condensation channels
- Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data
- Investigation on thermal-hydraulic performance prediction of a new parallel-flow shell and tube heat exchanger with different surrogate models
- Comparative study of the thermal performance of four different parallel flow shell and tube heat exchangers with different performance indicators
- Optimization of SCR inflow uniformity based on CFD simulation
- Kinetics and thermodynamics of SO2 adsorption on metal-loaded multiwalled carbon nanotubes
- Effect of the inner-surface baffles on the tangential acoustic mode in the cylindrical combustor
- Special Issue on Future challenges of advanced computational modeling on nonlinear physical phenomena - Part I
- Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications
- Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems
- Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics
- Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water
- Closed-form wave structures of the space-time fractional Hirota–Satsuma coupled KdV equation with nonlinear physical phenomena
- Some misinterpretations and lack of understanding in differential operators with no singular kernels
- Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics
- Calculation of focal values for first-order non-autonomous equation with algebraic and trigonometric coefficients
- Influence of interfacial electrokinetic on MHD radiative nanofluid flow in a permeable microchannel with Brownian motion and thermophoresis effects
- Standard routine techniques of modeling of tick-borne encephalitis
- Fractional residual power series method for the analytical and approximate studies of fractional physical phenomena
- Exact solutions of space–time fractional KdV–MKdV equation and Konopelchenko–Dubrovsky equation
- Approximate analytical fractional view of convection–diffusion equations
- Heat and mass transport investigation in radiative and chemically reacting fluid over a differentially heated surface and internal heating
- On solitary wave solutions of a peptide group system with higher order saturable nonlinearity
- Extension of optimal homotopy asymptotic method with use of Daftardar–Jeffery polynomials to Hirota–Satsuma coupled system of Korteweg–de Vries equations
- Unsteady nano-bioconvective channel flow with effect of nth order chemical reaction
- On the flow of MHD generalized maxwell fluid via porous rectangular duct
- Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation
- Numerical solution of two-term time-fractional PDE models arising in mathematical physics using local meshless method
- A powerful numerical technique for treating twelfth-order boundary value problems
- Fundamental solutions for the long–short-wave interaction system
- Role of fractal-fractional operators in modeling of rubella epidemic with optimized orders
- Exact solutions of the Laplace fractional boundary value problems via natural decomposition method
- Special Issue on 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
- Joint use of eddy current imaging and fuzzy similarities to assess the integrity of steel plates
- Uncertainty quantification in the design of wireless power transfer systems
- Influence of unequal stator tooth width on the performance of outer-rotor permanent magnet machines
- New elements within finite element modeling of magnetostriction phenomenon in BLDC motor
- Evaluation of localized heat transfer coefficient for induction heating apparatus by thermal fluid analysis based on the HSMAC method
- Experimental set up for magnetomechanical measurements with a closed flux path sample
- Influence of the earth connections of the PWM drive on the voltage constraints endured by the motor insulation
- High temperature machine: Characterization of materials for the electrical insulation
- Architecture choices for high-temperature synchronous machines
- Analytical study of air-gap surface force – application to electrical machines
- High-power density induction machines with increased windings temperature
- Influence of modern magnetic and insulation materials on dimensions and losses of large induction machines
- New emotional model environment for navigation in a virtual reality
- Performance comparison of axial-flux switched reluctance machines with non-oriented and grain-oriented electrical steel rotors
- Erratum
- Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”