Power Law Relationship Research Articles

Is Membrane Filtration Applicable for the Recovery of Biologically Active Substances from Spent Lavender?

This study explored the batch membrane filtration of 40% ethanol extracts from spent lavender, containing valuable compounds like rosmarinic acid, caffeic acid, and luteolin, using a polyamide-urea thin film composite X201 membrane. Conducted at room temperature and 20 bar transmembrane pressure, the process demonstrated high efficiency, with rejection rates exceeding 98% for global antioxidant activity and 93–100% for absolute concentrations of the target components. During concentration, the permeate flux declined from 2.43 to 1.24 L·m−2·h−1 as the permeate-to-retentate-volume ratio increased from 0 to 1. The process resistance, driven by osmotic pressure and concentration polarization, followed a power–law relationship with a power value of 1.20, consistent with prior nanofiltration studies of rosmarinic acid solutions. Notably, no membrane fouling occurred, confirming the method’s scalability without compromising biological activity. The antioxidant activity, assessed via the DPPH method, revealed that the retentate exhibited double the activity of the feed. Antibacterial assays using broth microdilution showed that the retentate inhibited Escherichia coli by 73–96% and Bacillus subtilis by 97–98%, making it the most active fraction. These findings validate the effectiveness of the X201 membrane for concentrating natural antioxidants and antibacterial agents from lavender extract under sustainable operating conditions.

Induced polarization of clay-rich materials — Part 4: Water content and temperature effects in bentonites

Deep geological disposals (DGDs) are widely seen to be the best solution to contain high-level radioactive wastes safely. Compacted bentonite and bentonite-sand mixtures are considered the most appropriate buffers or sealing materials for access drifts, ramps, and shafts due to their favorable physicochemical and hydromechanical properties. Bentonite-sand mixtures are expected to swell and seal all voids when in contact with water, forming an impermeable barrier to radioactive elements. The parameters that will most affect the hydraulic performance of these seals are their water content, dry density, water salinity, and temperature. Monitoring and assessing these parameters are, therefore, crucial to confirm that the seals’ safety functions are fulfilled during the life of a DGD. Induced polarization (IP) is a nonintrusive geophysical method able to perform this task. However, the underlying physics of bentonite-sand mixtures has not been checked. The complex conductivity spectra of 42 compacted bentonite-sand mixtures are measured in the frequency range of 1 Hz–45 kHz in order to develop workable relationships between in-phase and quadrature conductivities versus water content and saturation, pore water conductivity, bentonite-sand ratio (10% to 100%), temperature (10°C–60°C), and dry density (0.97 to 1.64 [Formula: see text]). We observe that conductivity is mostly dominated by surface conductivity associated with the Stern layer coating the surface of smectite, the main component of bentonite. At a given salinity and temperature, the in-phase and quadrature conductivities obey power law relationships with water content and saturation. The in-phase and quadrature conductivities depend on temperature according to a classical linear relationship with the same temperature coefficient. A Stern layer-based model is used to explain the dependence of the complex conductivity with water content, dry density, water salinity, and temperature. It could be used to interpret IP field data to monitor the efficiency of the seal of DGD facilities.

Scaling Behavior of Ionic Conductance Dependent on Surface Charge Inside a Single-Digit Nanopore.

The ionic conductance in a charged nanopore exhibits a power-law behavior in low salinity-as has been verified in many experiments (G0∝c0α)-which is governed by surface charges. The surface charge inside a nanopore determines the zeta potential and ion distributions, which have a significant impact on ion transport, especially in a single-digit nanopore with potential leakage. However, precisely measuring surface charge density in a single-digit nanopore remains a challenge. Here, we propose a methodology for exploring the power-law variation of ionic conductance, with potential leakage taken into account. We conducted experiments to measure the ionic current using silicon nitride nanopores and employed a continuous theory to explore the relationship between pore-bound concentration and surface charges. Considering that the influence of potential leakage on concentration follows a power-law relationship, we established a coefficient (α) to examine the controlling factors of potential leakage and modified the conductance model to obtain the ion mobility inside a nanopore.

Measuring Precipitation via Microwave Bands with a High-Accuracy Setup.

The urgent need for timely and accurate precipitation estimations in the face of ongoing climate change and the increasing frequency and/or intensity of extreme weather events underscores the necessity for innovative approaches. Recently, several studies have focused on estimating the precipitation rate through induced attenuation of radio frequency (RF) signals, which are abundant in modern communication systems. Most research has concentrated on frequencies exceeding 10 GHz, as attenuation at lower frequencies is minimal, posing measurement challenges. This study aims to confront this limitation by introducing a high-precision experimental setup capable of detecting this subtle attenuation at frequencies under 10 GHz. The setup includes a transmitter and receiver optimized for operation at 2.07, 4.63, and 6.22 GHz, where minimal worldwide research exists. A power resolution below 10-5 dB in preliminary measurements demonstrated its effectiveness in quantifying signal attenuation due to precipitation across the specified frequencies. Moreover, a strong power law relationship was observed between signal attenuation and precipitation rate for all three frequencies, while, as expected, the higher the frequency, the more pronounced the signal attenuation was.

Three-dimensional dosimetry using multiple-energy delivery and a single-layer detector for quality assurance in proton pencil beam scanning.

In Proton Therapy, the presence of implants along the beam path is known to potentially affect the dose distribution. The way such implants are managed in the planning process can vary in the different treatment planning systems (TPSs) and different centers. A specific validation procedure should be accomplished to verify the accuracy of TPS computation in these conditions and accept the applied process before treating patients. The aim of this study is to present a quality assurance (QA) tool in pencil beam scanning proton therapy by a method based on multiple-energy delivery and a single-layer two-dimensional detector and to apply it for verifying three-dimensional dose computation and correcting CT calibration in the presence of implants. Multiple-energy delivery with a single-layer detector (MESL) acquisitions were performed for 80 energy layers (70-150MeV), composed of equally weighted pencil beam spots. MESL measures were acquired using a two-dimensional MatriXX-IBA detector. A transformation of the energy modulation to spatial modulation was obtained by using the power-law relationship of initial energy and range. The setup design involved a reference configuration, allowing to compensate for potential offsets, and the same configuration with an additional phantom to be measured. Both setups were imaged by a CT scanner, and the dose was computed by the TPS. The comparison of TPS-computed and MESL-measured data of the phantom was performed by producing a 2D map of range-error. For testing the procedure, plastic slabs and rods made of tissue equivalent materials (TEMs), with known water equivalent path length (WEPL), were used. Range error mapping was then applied to verify dose computation with a titanium cylinder and a titanium implant. Numerical procedures were obtained by modifying at the TPS the segmented volume, or the value in the CT calibration curve for the titanium objects. The optimal values were then determined by identifying the one that minimizes residual range error. The results of the consistency test on the plastic slabs and the TEM rods showed differences between measured and expected WEPL below 1%, confirming the reliability of the method and the energy-spatial transformation. In the titanium cylinder, the optimal volume and the point in the calibration curve (relative to the titanium saturated value), to be used for TPS simulation is about the real size of the cylinder and the tabulated stopping power value. However, the optimal value to be assigned to the CT calibration curve might depend on the type and shape of the object, as they were different for the cylinder and the implant with screws. The availability of a QA tool, like the one presented, paves the way for systematic studies of all the parameters that impact computation accuracy, and the methods to improve the accuracy of TPS computation.

Modeling memory function of entangled photon and classical laser photon-count fluctuations using white noise integral analysis

Abstract This study investigates photon-count fluctuation dynamics of two light sources, namely a spontaneous parametric down-conversion (SPDC) light source and a 780 nm attenuated laser diode (LD). White noise integral with customizable memory function is used to model the mean square displacements (MSDs) and the probability density functions (PDFs) for both light sources. This approach overcomes the limitation of monofractal scaling of fractional Brownian motion (fBm) model characterized by a single Hurst exponent. The memory function used has an exponential-tempered power-law relation, parametrized by μ and β, where β modulates the extent of memory parameter μ. Although optical losses and detector inefficiencies degrade photon statistics to Poissonian at post-detection, our findings reveal notable memory effects at higher mean photon counts, especially in the SPDC source with memory parameter μ ≧ 1.00, compared to the classical LD, which remained relatively constant at μ ≦ 1.00. Both light sources shared similar correction parameters β, which indicates they have identical photon-count fluctuations at short time but diverge significantly at longer time. This work highlights the need for models beyond fBm, capable of capturing complex MSD behaviors of photon-count fluctuations.

Flat Friedmann-Lemaitre-Robertson-Walker Cosmological Model with Time-Dependent Cosmological Constant in Brans-Dicke Theory of Gravity

Recently, there has been much interest in investigating outstanding problems of cosmology with modified theories of gravity. The Brans-Dicke theory of gravity is one such theory developed by Brans and Dicke absorbing Mach’s principle into the General Theory of Relativity. In Brans-Dicke theory, gravity couples with a time-dependent scalar field ϕ through a coupling parameter ω. This theory reduces to the General Theory of Relativity if the scalar field ϕ is constant and the coupling parameter ω →∞. In this paper, we consider a flat Friedmann-Lemaıtre-Robertson-Walker (FLRW) universe with a time-dependent cosmological constant in Brans-Dicke theory of gravity. Exact solutions of the field equations are obtained by using a power law relation between the scale factor and the Brans-Dicke scalar field ϕ and by taking the Hubble parameter H to be a hyperbolic function of the cosmic time t. We study the cosmological dynamics of our model by graphically representing some important cosmological parameters such as the deceleration parameter, energy density parameter, equation of state parameter, jerk parameter, snap parameter, lerk parameter etc. The statefinder diagnostic pair of the model is also obtained and the validity of the four energy conditions, viz. the Strong energy condition (SEC), Weak energy condition (WEC), Dominant energy condition (DEC) and Null energy condition (NEC), is examined. We find that the universe corresponding to our model is expanding throughout its evolution and exhibits late time cosmic acceleration, which is in agreement with the current observational data.

Predictive control of pore architecture in ice-templated scaffolds via heat flux density modulation

Replicating the intricate architecture of native tissues remains a significant challenge in tissue engineering. Ice-templated biomimetic scaffolds possess controlled porosity that conveniently resembles the native parenchyma of many tissues. In this study, we investigate the relationship between the porous architecture of lyophilised collagen scaffolds and key processing parameters during production. We establish a predictive model that correlates specific lyophilisation conditions with the resulting pore sizes. Systematic variations in the freeze-drying conditions resulted in scaffolds with average pore sizes ranging from 46 μm to 251 μm, effectively matching the length scale of extracellular matrix features found in native tissues. We introduce the concept of heat flux density (HFD) at equilibrium as a metric for quantifying latent heat extraction efficiency during the freezing process. Our findings reveal a power law relationship between HFD at equilibrium and pore size, with an exponent of −0.44. This approach provides a non-destructive and non-intrusive method for precisely controlling pore architecture, advancing the potential for creating scaffolds that closely emulate the complex structures of native tissues.

Development of piezo-driven extensional rheometry with drop-on-demand head for dilute polymer solutions

To assess the extensional properties of viscoelastic liquids with low viscosity, we explored a method employing a piezoelectric drop-on-demand (DOD) head. This method ejected polymer solutions of dilute concentrations, which offered a higher suitability than the liquid dripping (LD) method. An exponentially decaying regime of filament diameter was observed, like the elasto-capillary regime of the LD method. The established power law relation between extensional relaxation time and polymer solution concentration holds in the dilute regime. The findings indicate that the filament decay behaviors observed for the DOD method with jetting flow and the LD method with dripping flow are comparable.

Magnetic structures in the explicitly time-dependent nontwist map.

We investigate how the magnetic structures of the plasma change in a large aspect ratio tokamak perturbed by an ergodic magnetic limiter, when a system parameter is non-adiabatically varied in time. We model such a scenario by considering the Ullmann-Caldas nontwist map, where we introduce an explicit time-dependence to the ratio of the limiter and plasma currents. We apply the tools developed recently in the field of chaotic Hamiltonian systems subjected to parameter drift. Namely, we follow trajectory ensembles initially forming Kolmogorov Arnold Moser (KAM) tori and island chains in the autonomous configuration space. With a varying parameter, these ensembles, called snapshot tori, develop time-dependent shapes. An analysis of the time evolution of the average distance of point pairs in such an ensemble reveals that snapshot tori go through a transition to chaos, with a positive Lyapunov exponent. We find empirical power-law relationships between both the Lyapunov exponent and the beginning of the transition to chaos (the so-called critical instant), as a function of the rate of the parameter drift, with the former showing an increasing trend and the latter a decreasing trend. We conclude that, in general, coherent tori and magnetic islands tend to break up and become chaotic as the perturbation increases, similar to the case of subsequent constant perturbations. However, because of the continuous drift, some structures can persist longer and exist even at perturbation values where they would not be observable in the constant perturbation case.

Penetration of jet piles on submerged granular beds

The study examines the dynamics of jet pile penetration into submerged granular beds through laboratory experiments with the jet pile positioned atop the granular bed. It examines how varying water jet velocities affect penetration depth across different pile diameters and granular media sizes. Results show that high-velocity water jets locally fluidize particles around the pile, reducing inter-particle resistance within the bed, which, in turn, cannot support the self-weight of the pile, allowing smoother penetration. The onset of fluidization and pile penetration, marked by a critical jet velocity, increases with bed depth. Jet pile penetration is governed by a balance of forces: water jet force (FJet), pile self-weight (Fsw), buoyancy (FB), and resistance from the granular bed (FR). A power law relationship is proposed to predict penetration depth across different grain and pile sizes, providing a predictive model for jet pile penetration depth. This scaling law, validated with another experimental study, demonstrates consistent accuracy.

Radial Evolution of Non-Maxwellian Electron Populations Derived from Quasi-thermal Noise Spectroscopy: Parker Solar Probe Observations

Understanding the transport of energy within space plasmas, particularly in the solar wind, remains a complex challenge. Accurate measurement of electron temperatures and their nonthermal characteristics is crucial for comprehending energy transport properties in plasmas. Quasi-thermal-noise (QTN) spectroscopy has emerged as a dependable tool for precise electron parameters assessment as it is less susceptible to spacecraft effects than particle detectors. In this study, we apply a QTN spectroscopy fitting method to analyze data from the Parker Solar Probe FIELDS radio instrument obtained during Encounters 2 through 13, under unbiased antenna conditions. We use the kappa function to characterize the electron velocity distribution and employ a fitting technique to derive the changes in each parameter across heliocentric distances ranging from 12 Rs to 76 Rs. Specifically, we find that the electron density scales as n e ∝ r −2.09±0.04 and the T e ∝ r −0.65±0.02. The distribution of the kappa index has three distinct regions as a function of radial distance from the Sun. Furthermore, we conduct a statistical analysis of solar wind energy flux which we finds follows a power-law relationship w total ∝ r −1.92±0.04.

A Parameter Study of 1D Atmospheric Models of Pulsating AGB Stars

Using the atmospheric pulsation code written by George Bowen, we have performed a parameter study examining the effects of modifying various parameters of models of oxygen-rich AGB atmospheres pulsating in the fundamental and first-overtone modes. For each pulsation mode, we have examined the effects of adjusting the dust condensation temperature, dust condensation temperature range, pulsation amplitude, dust opacity, and metallicity. Our model grids are generated with the constraint that their luminosities are chosen to span the range of observed mass loss rates at a chosen mass. The dust condensation temperature, pulsation amplitude, and dust opacity have strong effects on the ultimate location and shape of the final model grids in the mass luminosity plane. The mass loss rate evolution of the fundamental and first-overtone mode models show a significant difference in behavior. While the fundamental mode models exhibit the typically assumed power–law relation with mass and luminosity, the first-overtone mode models show significant non-power law behavior at observed mass loss rates. Effectively, models in the first-overtone mode require somewhat higher luminosities to reach the same mass loss rates seen in fundamental mode models of the same mass, consistent with observed AGB stars.

Dynamic in-situ CT imaging to study meso-structure evolution and fracture mechanism of shale during thermal-mechanical coupling condition

Temperature has a significant impact on the occurrence characteristics and flow properties of oil and gas in shale reservoirs at in-situ conditions. Under thermal–mechanical coupling conditions, the macroscopic deformation instability characteristics and the evolution of the internal microstructure of shale are of great importance for the exploitation of shale oil and gas. However, most studies on the macroscopic and microscopic characteristics of shale only analyze the deformation and instability mechanisms of shale from observations of the post-failure microscopic structures. This paper employs a self-developed THM-CT coupling test system to study the macroscopic deformation characteristics of shale under triaxial compression at real-time temperatures, and simultaneously uses in-situ CT imaging technology to characterize the internal microstructure of shale under different stress levels. Real-time CT porosity obtained via in-situ CT imaging technology represents the mesoscopic structural parameters, together with macroscopic deformation characteristics, delineate the four stages of the entire deformation process in shale: initial compression, linear elastic deformation, yielding deformation, and post-failure. The deformation after peak-stress (σf) in shale is 1–3 times that before peak-stress (σf). The dissolution and softening of clay minerals within the internal micro-lamination of shale, along with the weakening of the internal structure, result in a decline in mechanical parameters such as stress strength (σf) and elastic modulus (E) with increasing temperature. The reconstruction of three-dimensional μCT digital volumes further reconstructs the internal fracture spatial structure under different stress levels during the deformation process, precisely characterizing the dynamic evolution of internal fracture nucleation, expansion, and coalescence during the whole test process. The failure characteristics of shales display notable heterogeneity and anisotropy. Internally, fractures experience a sequence of initiation, formation of vertical and oblique main fractures along the axial direction, and crossing connections between fractures. During test process, multiple occurrences of horizontal secondary micro-fractures extend along weakly cemented lamination, playing a connecting role between the main fractures. Importantly, a real-time quantitative relationship between the macroscopic and microscopic mechanics of rock has been established by linking the mesoscopic damage factor with the applied stress. It was found that the damage factor increases according to a power-law relationship with stress in the yield deformation phase. The variation in the mesoscopic damage factor serves as an intuitive index reflecting the systematic failure of rock, providing an early warning for the impending failure of shale.

Behavioural response of chub, barbel and brown trout to pulsed direct current electric fields

Electrified fish guidance and trash racks at water intakes are a promising technology to divert downstream moving fish away from turbines and towards a safe bypass route. Current recommendations on pulsed direct current (pDC) waveforms to electrify such racks are based on a limited number of field studies, and hence investigations comparing pDC waveforms are needed. To this end, systematic tests of electrosensitivity to pDC waveforms were performed with wild caught brown trout (Salmo trutta), chub (Squalius cephalus) and barbel (Barbus barbus) to determine (1) behaviour types and thresholds exhibited by different species and variation within species families, (2) the effect of fish body size, and (3) optimal parameters of pDC waveforms for possible use at electrified bar racks. Both the peak power density threshold triggering immobilization and twitch reactions decreased with increasing fish size according to a power law relation. Increasing frequency led to lower thresholds for immobilization and higher thresholds for twitch reactions. Though some inter-specific variation was observed, a waveform with a pulse duration of 2 ms and a frequency of 10 Hz was determined to be the most promising for all three species to be tested and possibly used at electrified bar racks.

A framework for generating rating curves in Mahanadi River using hydrodynamic model and radar altimetry data

ABSTRACT The limited availability of in-situ data has drawn attention towards using remote sensing techniques to monitor river flow. Radar altimetry data has been used to generate stage-discharge rating curves through power-law relations and empirical methods. However, evaluating hydrodynamic models for rating curve generation using multi-mission altimetry data in data-scarce regions is lacking. We used altimetry data (Jason 2, Jason 3, SARAL/AltiKa, Sentinel 3A, and Sentinel 3B) over the Mahanadi River to evaluate rating curves at virtual stations. The HEC-RAS hydrodynamic model was set up, identifying seven virtual stations along the Mahanadi River from Boudh to Mundali Barrage. Statistical evaluation of ‘water level’ (RMSE 0.27-0.88 m) and ‘discharge’ (KGE 0.52 to 0.88) components of the generated rating curves showed significant agreement with radar altimetry data. These rating curves at virtual stations offer a cost-effective tool for monitoring river flows at additional locations.

Three-dimensional clustering characteristics of large-Stokes-number dilute sprays interacting with turbulent swirling co-flows

Three-dimensional (3-D) clustering characteristics of large-Stokes-number sprays interacting with turbulent swirling co-flows are investigated experimentally. The astigmatic interferometric particle imaging (AIPI) technique is used for simultaneous measurement of the spray droplets position in 3-D space and their corresponding diameter. The Stokes number estimated based on the Kolmogorov time scale varies from 34 to 142. The results show that the degree of droplet clustering plateaus at about 0.4 and at large Stokes numbers. It is obtained that the mean length scale of the clusters normalized by the Kolmogorov length scale follows a power-law relation, and the mean void length scale normalized by the integral length scale plateaus at about 1.5 and at large Stokes numbers. It is shown that the ratio of the number density of the droplets residing within the clusters to the global number density increases with increasing Stokes number and is about 8 for the largest Stokes number examined in this study. The joint characteristics of cluster's normalized volume and the mean diameter of droplets residing within the clusters show that small-volume clusters accommodate droplets with a relatively broad range of diameters. However, large clusters carry droplets with the most probable diameter. The developed AIPI technique in the present study and the corresponding spray characteristics are of importance for engineering applications that aim to understand the 3-D clustering characteristics of large-Stokes-number droplets sprayed into turbulent swirling co-flows.

Nanoscale mapping of local intrinsic strain-induced anomalous bandgap variations in WSe2 using selective-wavelength scanning photoconductivity microscopy

Nanoscale defects can locally tailor the optoelectronic properties of two-dimensional materials such as bandgap. However, it is still challenging to directly map and analyze the defect-induced bandgap variations in a quantitative manner. Here, we report the nanoscale mapping of local intrinsic strain-induced anomalous bandgap variations in as-grown WSe2 by using a selective-wavelength scanning photoconductivity microscopy. In this method, a conducting nanoprobe is utilized to map the spatial distributions of strain, sheet-conductance, and charge trap density (Neff) of epitaxially-grown WSe2 on sapphire while illuminating monochromatic light of selective wavelengths. Under un-illuminated conditions, the maps showed WSe2 domain structures with boundaries having slightly lower sheet-conductance and higher Neff than those in domains, presumably due to low misorientation angles between adjacent epitaxially-grown domains. By measuring wavelength-dependent photoconductance maps and fitting each pixel value of the maps, we could successfully obtain the map of local bandgap. The map clearly showed bandgap variations inside domains as well as rather low bandgaps at boundaries. By comparing with local strain map, we found that tensile strain effectively reduced bandgap following two different power-law relationships. Such anomalous bandgap variations in WSe2 could be explained by strain-induced weakening of d-orbital couplings. Furthermore, in a monolayer-bilayer WSe2 interface, bilayer WSe2 exhibited lower bandgap than the underlying monolayer WSe2, while interfacial boundaries exhibited the strain-induced bandgap values in between those of monolayer and bilayer WSe2. Since our method allows us to directly map the intrinsic strain-induced bandgap variations with a nanoscale resolution down to tens-of-nm, it can be a powerful tool for basic research and practical applications of optoelectronic devices based on two-dimensional materials.

Stability of synchronization manifolds and its nonlinear behaviour in memristive coupled discrete neuron model.

In this study, we investigate the impact of first and second-order coupling strengths on the stability of a synchronization manifold in a Discrete FitzHugh-Nagumo (DFHN) neuron model with memristor coupling. Master Stability Function (MSF) is used to estimate the stability of the synchronized manifold. The MSF of the DFHN model exhibits two zero crossings as we vary the coupling strengths, which is categorized as class . Interestingly, both zero-crossing points demonstrate a power-law relationship with respect to both the first-order coupling strength and flux coefficient, as well as the second-order coupling strength and flux coefficient. In contrast, the zero crossings follow a linear relationship between first-order and second-order coupling strength. These linear and nonlinear relationships enable us to forecast the zero-crossing point and, consequently, determine the coupling strengths at which the stability of the synchronization manifold changes for any given set of parameters. We further explore the regime of the stable synchronization manifold within a defined parameter space. Lower values of both first and second-order coupling strengths have minimal impact on the transition between stable and unstable synchronization regimes. Conversely, higher coupling strengths lead to a shrinking regime of the stable synchronization manifold. This reduction follows an exponential relationship with the coupling strengths. This study is helpful in brain-inspired computing systems by understanding synchronization stability in neuron models with memristor coupling. It helps to create more efficient neural networks for tasks like pattern recognition and data processing.

An Analytical Study of Tsunamis Generated by Submarine Landslides

In this work, the problem of tsunamis generated by underwater landslides is addressed. Two new solutions are derived in the framework of the linear shallow water equations and linear potential wave theory, respectively. Those solutions are analytical (1 + 1D) and another is semi-analytical (2 + 1D). The 1 + 1D model considers a solid body sliding over a sloping beach at a constant speed, and the 2 + 1D model considers a solid landslide that moves at a constant velocity on a flat bottom. The solution 1 + 1D is checked numerically using a different finite scheme. The 2 + 1D model examines the kinematic and geometric features of the landslide at a constant ocean depth and its influence on the generation of tsunamis. Landslide geometry significantly influences run-up height. Our results reveal a power law relationship between normalized run-up and landslide velocity within a realistic range and a negative power law for the landslide length–thickness. Additionally, a critical aspect ratio between the length and width of the sliding body is identified, which enhances the tsunamigenic process. Finally, the results show that the landslide shape does not have a decisive influence on the pattern of tsunami wave generation and propagation.