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Several reports about infinite-layer nickelate thin films suggest that the superconducting critical temperature versus chemical doping phase diagram has a dome-like shape, similar to cuprates. Here, we demonstrate a highly reproducible superconducting state in undoped PrNiO$_2$ thin films grown onto SrTiO$_3$. Scanning transmission electron microscopy measurements demonstrate coherent and defect-free infinite-layer phase, a high structural quality with no unintentional chemical doping and a total absence of interstitial oxygen. X-ray absorption measurements show very sharp features at the Ni L$_{3,2}$-edges with a large linear dichroism, indicating the preferential hole-occupation of Ni$^{1+}$-3d$_{x^2-y^2}$ orbitals in a square planar geometry. Resonant inelastic X-ray scattering measurements reveal sharp magnon excitations of 200\,meV energy at magnetic Brillouin zone boundary, highly resonant at the Ni$^{1+}$ absorption peak. The results indicate that, when properly stabilized, infinite-layer nickelate thin films are superconducting without chemical doping.

In two-dimensional electron systems (2DES) the breaking of the inversion, time-reversal and bulk crystal-field symmetries is interlaced with the effects of spin-orbit coupling (SOC) triggering exotic quantum phenomena. Here, we used epitaxial engineering to design and realize a 2DES characterized simultaneously by ferromagnetic order, large Rashba SOC and hexagonal band warping at the (111) interfaces between LaAlO$_{3}$, EuTiO$_{3}$ and SrTiO$_{3}$ insulators. The 2DES displays anomalous quantum corrections to the magneto-conductance driven by the time-reversal-symmetry breaking occurring below the magnetic transition temperature. The results are explained by the emergence of a non-trivial Berry phase and competing weak anti-localization / weak localization back-scattering of Dirac-like fermions, mimicking the phenomenology of gapped topological insulators. These findings open perspectives for the engineering of novel spin-polarized functional 2DES holding promises in spin-orbitronics and topological electronics.

We use Resonant Inelastic X-ray Scattering (RIXS) to compare the doping dependence of magnetic excitations of an Infinite-Layer nickelate to those of a prototypical superconducting cuprate. The polarization analysis of RIXS spectra establishes the dominant spin-flip nature of the mid-infrared peak in both cases. Hole doping leads to opposite behavior of the magnetic energy in the two materials. By fitting the data with an original Hubbard-based model for dynamic susceptibility, we find that t is comparable in the two materials while U is about twice larger in the nickelate. This finding accounts for the smaller magnetic bandwidth of nickelates and for its decrease upon doping., Comment: 7 pages with bibliography, 4 figures

Following the discovery of superconductivity in hole-doped NdNiO$_2$ infinite-layer thin films, extensive research has been conducted particularly to compare these materials with cuprates. Superconductivity has also been observed in nickelate thin films with other rare-earth elements like Pr and La, but not in their bulk forms, suggesting a critical role for substrate-induced strain/interface or dimensionality effects. In this study, we use water-soluble (Ca,Sr)$_3$Al$_2$O$_6$ sacrificial layers to fabricate freestanding perovskite nickelate membranes and explore topotactic reduction without the SrTiO$_3$ substrate as a template. NdNiO$_3$-based heterostructure membranes transferred from a LaAlO$_3$ substrate exhibit better metallic behavior and higher hysteresis than those transferred from SrTiO$_3$, owing to the different strain states that the NdNiO$_3$ layer experience when grown on these two substrates. Despite the expected X-ray diffraction shifts, membranes reduced with CaH$_2$ display insulating characteristics, similar to bulk infinite-layer nickelates. Our findings strongly indicate that a template is necessary to stabilize a coherent and robust infinite-layer phase with optimal transport properties.

We report an experimental study of the magnetic properties of infinite-layer Nd1-xSrxNiO2 thin films by x-ray magnetic circular dichroism (XMCD) at Ni L3,2 and Nd M5,4 edges. We show that at low temperatures the out-of-plane component of the Ni1+ spin-moment is characterized by a rapid increase for magnetic fields below 1T , followed by a slower linear increase reaching a spin-moment value of 0.25uB/Ni at 9T in the case of superconducting Nd0.8Sr0.2NiO2. On the other hand, the Nd M5,4 XMCD shows a clear paramagnetic behaviour, which make both Ni- and Nd-spin-sublattices fully uncorrelated.The magnetic field and temperature dependencies of the Ni L3,2 XMCD data can be explained by assuming an out-of-plane canting of the strongly in-plane anti-ferromagnetic ordered Ni1+ spins. A symmetry lowering of the NiO2 planes observed via four-dimensional scanning transmission electron microscopy, triggering a DMI, can be responsible of the proposed Ni1+ spin-canting at zero-field. The resulting out-of-plane weak-ferromagnetic coupling under magnetic field explains the relatively large spin-moment and its magnetic field and temperature dependence.

We report scanning tunnelling microscopy (STM) and x-ray photoemission spectroscopy (XPS) measurements on uncapped and SrTiO3 (STO) capped NdNiO2 realized by pulsed-laser deposition and topotactic reduction process. We find that untreated NdNiO2 surfaces are insulating and contain Ni mostly in a nominal Ni2+ oxidation state. Room temperature STM shows signatures of a striped-like topographic pattern, possibly compatible with recent reports of ordered oxygen vacancies in uncapped nickelates due to incomplete oxygen de-intercalation of the upper layers. A metallic surface and a full Ni1+ oxidation state is recovered by ultra high vacuum annealing at 250 C, as shown by STM and XPS. STO-capped NdNiO2 films, on the other hand, show Ni mostly in Ni1+ configuration, but Nd 3d5/2 core level spectra have a relevant contribution from ligand 4f 4L states, suggesting the formation of a NdTiNiOx layer at the interface with the STO. By in situ unit-cell by unit-cell Ar-ion sputtering removal of the STO capping and of the non stoichiometric interface layer, we were able to address the surface electronic properties of these samples, as shown by high resolution valence band photoemission spectroscopy. The results provide insights in the properties of infinite-layer NdNiO2 thin films prepared by the CaH2 topotactic reduction of perovskite NdNiO3 and suggest methods to improve their surface quality.

Spin-orbit coupling and breaking of inversion symmetry are necessary ingredients to enable a pure spin current-based manipulation of the magnetization via the spin-orbit torque effect. Currently, magnetic insulator oxides with non-dissipative characteristics are being explored. When combined with non-magnetic heavy metals, known for their large spin-orbit coupling, they offer promising potential for energy-efficient spin-orbitronics applications. The intrinsic electronic correlations characterizing those strongly correlated oxides hold the promises to add extra control-knobs to the desired efficient spin-wave propagation and abrupt magnetization switching phenomena. Spinel vanadate FeV2O4 (FVO) exhibits several structural phase transitions which are accompanied by an intricate interplay of magnetic, charge and orbital orderings. When grown as a thin film onto SrTiO3, the compressive strain state induces a perpendicular magnetic anisotropy, making FVO-based heterostructures desirable for spin-orbitronics applications. In this study, we have optimised the deposition of stoichiometric and epitaxial Pt/FVO heterostructures by Pulsed Laser Deposition and examined their spin-related phenomena. From angle-dependent magnetotransport measurements, we observed both Anisotropic Magnetoresistance (AMR) and Spin Hall Magnetoresistance (SMR) effects. Our findings show the SMR component as the primary contributor to the overall magnetoresistance, whose high value of 0.12% is only comparable to properly optimized oxide-based systems.

Charge ordering (CO) phenomena have been widely debated in strongly-correlated electron systems mainly regarding their role in high-temperature superconductivity. Here, we elucidate the structural and charge distribution in NdNiO$_{2}$ thin films prepared with and without capping layers, and characterized by the absence and presence of CO. Our microstructural and spectroscopic analysis was done by scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) and hard x-ray photoemission spectroscopy (HAXPES). Capped samples show Ni$^{1+}$, with an out-of-plane (o-o-p) lattice parameter of around 3.30 angstroms indicating good stabilization of the infinite-layer structure. Bulk-sensitive HAXPES on Ni-2p shows weak satellite feature indicating large charge-transfer energy. The uncapped samples evidence an increase of the o-o-p parameter up to 3.65 angstroms on the thin-film top, and spectroscopies show signatures of higher valence in this region (towards Ni$^{2+}$). Here, 4D-STEM demonstrates (3,0,3) oriented stripes which emerge from partially occupied apical oxygen. Those stripes form quasi-2D coherent domains viewed as rods in the reciprocal space with $\Delta\text{q}_{z} \approx 0.24$ r.l.u. extension located at Q = ($\pm \frac{1}{3},0,\pm \frac{1}{3}$) r.l.u. and Q = ($\pm \frac{2}{3},0,\pm \frac{2}{3}$) r.l.u. The stripes associated with oxygen re-intercalation concomitant with hole doping suggests a possible link to the previously reported CO in infinite-layer nickelate thin films.

Gamma-Flash is an Italian project funded by the Italian Space Agency (ASI) and led by the National Institute for Astrophysics (INAF), devoted to the observation and study of high-energy phenomena, such as terrestrial gamma-ray flashes and gamma-ray glows produced in the Earth's atmosphere during thunderstorms. The project's detectors and the data acquisition and control system (DACS) are placed at the "O. Vittori" observatory on the top of Mt. Cimone (Italy). Another payload will be placed on an aircraft for observations of thunderstorms in the air. This work presents the architecture of the data acquisition and control system and the data flow., Comment: 4 pages, 1 figure, Astronomical Data Analysis Software and System XXXII (2022)

Recent biological experiments have shown that certain types of cells are able to move in structured and confined environment even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works, we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nucleus membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results can be potentially useful in determining the physical limit of cell migration in confined environment and in designing scaffold for tissue engineering.

The recent discovery of a zero-resistance state in nickel-based compounds has generated a re-excitement about the long-standing problem in condensed matter of high-critical-temperature superconductivity, in light of the analogies between infinite-layer nickelates and cuprates. However, despite some formal valence and crystal symmetry analogies, the electronic properties of infinite-layer nickelates are remarkably original accounting, among other properties, of a unique Nd5d-Ni3d hybridization. This designates infinite-layer nickelates as a new class of oxide superconductors which should be considered on their own. Here we report about Nd1-xSrxNiO2 (x = 0, 0.05 and 0.2) thin films synthesized with and without a SrTiO3 capping-layer, showing very smooth and step-terraced surface morphologies. Angle-dependent anisotropic magnetoresistance measurements performed with a magnetic field rotating in-plane or out-of-plane with respect to the sample surface, rendered important information about the magnetic properties of undoped SrTiO3-capped and uncapped samples. The results point at a key role of the capping-layer in controlling the magnitude and the anisotropy of the anisotropic magnetoresistance properties. We discuss this control in terms of a combined effect between the Nd-Ni hybridization and an intra-atomic exchange coupling between the Nd-4f and Nd-5d states, the latter essentially contributing to the (magneto)transport. Further studies foresee the influence of the capping layer on infinite-layer nickelates with no magnetic rare-earth.

A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper modeling assumptions the capillaries are reduced to their centerline: a well posed mathematical model is hence worked out, based on the coupling between a three-dimensional and a one-dimensional equation (3D-1D coupled problem). Also the application of a PDE-constrained optimization formulation is here proposed for the first time for angiogenesis simulations. Under this approach no mesh conformity is required, thus making the method particularly suitable for this kind of application, since no remeshing is required as the capillary network grows. In order to handle both the evolution of the quantities of interest and the changes in the geometry, a discrete-hybrid strategy is adopted, combining a continuous modeling of the tissue and of the chemicals with a discrete tip-tracking model to account for the vascular network growth. The tip-tracking strategy, together with some proper rules for branching and anastomosis, is able to provide a realistic representation of the capillary network.

Understanding the polarization switching mechanisms at play in ferroelectric materials is crucial for their exploitation in electronic devices. The conventional centrosymmetric reference structure-based mechanism which accounts for ferroelectricity in most of the usual displacive ferroelectric materials is too energy-demanding for some newly diagnosed ferroelectric materials such as the Ga2-xFexO3 (0.8 < x < 1.4) compounds. Some alternative theoretical propositions have been made and need experimental confirmation. A dual-scale electron microscopy study is performed on thin films of the Ga0.6Fe1.4O3 multiferroic compound. A wide scale precession-assisted electron diffraction tomography study first allows the determination of the structure the compound adopts in thin films, and even permits the refinement of the atomic positions within this structure. Cationic mobility is suggested for two of the atomic positions through the existence of extra electronic density. A local in situ high resolution scanning transmission electron microscopy study then allows confirming these mobilities by directly spotting the cationic displacements on successively acquired images. The whole study confirms an unconventional switching mechanism via local domain wall motion in this compound.

In recent years, multifunctional materials have attracted increasing interest for magnetic memories and energy harvesting applications. Magnetic insulating materials are of special interest for this purpose, since they allow the design of more efficient devices due to the lower Joule heat losses. In this context, Ga$_{0.6}$Fe$_{1.4}$O$_3$ (GFO) is a good candidate for spintronics applications, since it can exhibit multiferroicity and presents a spin Hall magnetoresistance similar to the one observed in a yttrium iron garnet (YIG)/Pt bilayer. Here, we explore GFO utilizing thermo-spin measurements in an on-chip approach. By carefully considering the geometry of our thermo-spin devices we are able to quantify the spin Seebeck effect and the spin current generation in a GFO/Pt bilayer, obtaining a value comparable to that of YIG/Pt. This further confirms the promises of an efficient spin current generation with the possibility of an electric-field manipulation of the magnetic properties of the system in an insulating ferrimagnetic material.

The low power manipulation of magnetization is currently a highly sought-after objective in spintronics. Non ferromagnetic large spin-orbit coupling heavy metal (NM) / ferromagnet (FM) heterostructures offer interesting elements of response to this issue, by granting the manipulation of the FM magnetization by the NM spin Hall effect (SHE) generated spin current. Additional functionalities, such as the electric field control of the spin current generation, can be offered using multifunctional ferromagnets. We have studied the spin current transfer processes between Pt and the multifunctional magnetoelectric Ga0.6Fe1.4O3 (GFO). In particular, via angular dependent magnetotransport measurements, we were able to differentiate between magnetic proximity effect (MPE)-induced anisotropic magnetoresistance (AMR) and spin Hall magnetoresistance (SMR). Our analysis shows that SMR is the dominant phenomenon at all temperatures and is the only one to be considered near room temperature, with a magnitude comparable to those observed in Pd/YIG or Pt/YIG heterostructures. These results indicate that magnetoelectric GFO thin films show promises for achieving an electric-field control of the spin current generation in NM/FM oxide-based heterostructures.

Superconductivity in infinite-layer nickelates holds exciting analogies with that of cuprates, with similar structures and $3d$-electron count. Using resonant inelastic x-ray scattering (RIXS) we studied electronic and magnetic excitations and charge density correlations in Nd$_{1-x}$Sr$_{x}$NiO$_2$ thin films with and without an SrTiO$_3$ capping layer. We observe dispersing magnons only in the capped samples, progressively dampened at higher doping. In addition, we detect an elastic resonant scattering peak in the uncapped $x=0$ compound at wave vector (1/3,0), remindful of the charge order signal in hole doped cuprates. The peak weakens at $x=0.05$ and disappears in the superconducting $x=0.20$ film. The uncapped samples also present a higher degree of Ni$3d$-Nd$5d$ hybridization and a smaller anisotropy of the Ni$3d$ occupation with respect to the capped samples. The role of the capping on the possible hydrogen incorporation or on other mechanisms responsible for the electronic reconstruction far from the interface remains to be understood.

Multi-orbital physics in quasi-two-dimensional electron gases (q2DEGs) triggers unique phenomena not observed in bulk materials, such as unconventional superconductivity and magnetism. Here, we investigate the mechanism of orbital selective switching of the spin-polarization in the oxide q2DEG formed at the (001) interface between the LaAlO$_{3}$, EuTiO$_{3}$ and SrTiO$_{3}$ band insulators. By using density functional theory calculations, transport, magnetic and x-ray spectroscopy measurements, we find that the filling of titanium-bands with 3d$_{xz,yz}$ orbital character in the EuTiO3 layer and at the interface with SrTiO$_{3}$ induces an antiferromagnetic to ferromagnetic switching of the exchange interaction between Eu-4f$^{7}$ magnetic moments. The results explain the observation of the carrier density dependent ferromagnetic correlations and anomalous Hall effect in this q2DEG, and demonstrate how combined theoretical and experimental approaches can lead to a deeper understanding of novel electronic phases and serve as a guide for the materials design for advanced electronic applications.

Experiments show that when a monolayer of cells cultured on an elastic substrate is subject to a cyclic stretch, cells tend to re-orient either perpendicularly or at an oblique angle with respect to the main direction of the stretch. Due to stochastic effects, however, the distribution of angles achieved by the cells is broader and, experimentally, histrograms over the interval [0, 90] are reported. Here we will determine the evolution and the stationary state of probability density functions describing the statistical distribution of the orientations of the cells using Fokker-Planck equations derived from microscopic rules for the evolution of the orientation of the cell. As a first attempt, we shall use a stochastic differential equation related to a very general elastic energy and we will show that the results of the time integration and of the stationary state of the related forward Fokker-Planck equation compare very well with experimental results obtained by different researchers. Then, in order to model more accurately the microscopic process of cell re-orientation, we consider discrete in time random processes that allow to recover Fokker- Planck equations through the well known technique of quasi-invariant limit. In particular, we shall introduce a non-local rule related to the evaluation of the state of stress experienced by the cell extending its protrusions, and a model of re-orientation as a result of an optimal control internally activated by the cell. Also in the latter case the results match very well with experiments.

We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion.

The electric-field control of $d$-electron magnetism in multiferroic transition metal oxides is attracting widespread interest for the underlying fundamental physics and for next generation spintronic devices. Here, we report an extensive study of the $3d$ magnetism in magnetoelectric Ga$_{0.6}$Fe$_{1.4}$O$_3$ (GFO) epitaxial films by polarization dependent x-ray absorption spectroscopy. We found a non-zero integral of the x-ray magnetic circular dichroism, with a sign depending upon the relative orientation between the external magnetic field and the crystallographic axes. %By reliably enlarging the limit of the spin and orbital sum rules, which usually holds for materials where the magnetic ions exhibit a unique crystal field symmetry This finding translates in a sign-reversal between the average Fe magnetic orbital and spin moments. Large Fe-displacements, among some of the octahedral sites, lower the symmetry of the system producing anisotropic paths for the Fe-O bondings giving rise to a large orbital-lattice interaction akin to a preferential crystallographic direction for the magnetic orbital moment. The latter may lead to a partial re-orientation of the magnetic orbital moment under an external magnetic field that, combined to the ferrimagnetic nature of the GFO, can qualitatively explain the observed sign-reversal of the XMCD integral. The results suggest that a control over the local symmetry of the oxygen octahedra in transition metal oxides can offer a suitable leverage over the manipulation of the effective orbital and spin moments in magnetoelectric systems.

The mathematical modeling of tumor growth has a long history, and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using mathematical tools from statistical physics. To this extent, we introduce a novel kinetic model of growth which highlights the role of microscopic transitions in determining a variety of equilibrium distributions. At variance with other approaches, the mesoscopic description in terms of elementary interactions allows to design precise microscopic feedback control therapies, able to influence the natural tumor growth and to mitigate the risk factors involved in big sized tumors. We further show that under a suitable scaling both the free and controlled growth models correspond to Fokker--Planck type equations for the growth distribution with variable coefficients of diffusion and drift, whose steady solutions in the free case are given by a class of generalized Gamma densities which can be characterized by fat tails. In this scaling the feedback control produces an explicit modification of the drift operator, which is shown to strongly modify the emerging distribution for the tumor size. In particular, the size distributions in presence of therapies manifest slim tails in all growth models, which corresponds to a marked mitigation of the risk factors. Numerical results confirming the theoretical analysis are also presented.

Studies on oxide quasi-two dimensional electron gas (q2DEG) have been a playground for the discovery of novel and sometimes unexpected phenomena, like the reported magnetism at the surface and at the interface between LaAlO$_{3}$ and SrTiO$_{3}$ non-magnetic materials. However, magnetism in this system is weak and there are evidences of a not intrinsic origin. Here, by using in-situ high-resolution angle resolved photoemission we demonstrate that ferromagnetic EuTiO$_{3}$, the magnetic counterpart of SrTiO$_{3}$ in the bulk, hosts a q2DEG at its (001) surface. This is confirmed by density functional theory calculations with Hubbard U terms in the presence of oxygen divacancies in various configurations, all of them leading to a spin-polarized q2DEG related to the ferromagnetic order of Eu-4f magnetic moments. The results suggest EuTiO$_{3}$(001) as a new material platform for oxide q2DEGs, characterized by broken inversion and time reversal symmetries., Comment: Main text: 8 pages, 4 figures; Supplementary Materials: 11 pages, 11 figures

The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results from modulation of one non-dimensional parameter that depends on the tumbling frequency, the sensing radius, the mean speed in a given direction, the uniform configuration density and the tactic response to the cell density. Numerical simulations show that our linear stability analysis predicts quite precisely the ranges of parameters determining instability and pattern formation. We also extend the stability analysis in the case of different mean speeds in different directions. In this case, for parameter values leading to instability travelling wave patterns develop.

Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell overcrowding may hamper cells from moving in certain directions or even from sensing beyond regions that practically act like physical barriers. We extend the non-local kinetic model proposed by Loy and Preziosi (2019) to include situations in which the sensing radius is not constant, but depends on position, sensing direction and time as cells' behavior might be determined on the basis of information collected before reaching physically limiting configurations. We analyze how the actual possible sensing of the environment influences the dynamics by recovering the appropriate macroscopic limits and by integrating numerically the kinetic transport equation.

Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics. We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.

We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.